--- _id: '14888' abstract: - lang: eng text: 'A face in a curve arrangement is called popular if it is bounded by the same curve multiple times. Motivated by the automatic generation of curved nonogram puzzles, we investigate possibilities to eliminate the popular faces in an arrangement by inserting a single additional curve. This turns out to be NP-hard; however, it becomes tractable when the number of popular faces is small: We present a probabilistic FPT-approach in the number of popular faces.' acknowledgement: 'This work was initiated at the 16th European Research Week on Geometric Graphs in Strobl in 2019. A.W. is supported by the Austrian Science Fund (FWF): W1230. S.T. has been funded by the Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035]. A preliminary version of this work has been presented at the 38th European Workshop on Computational Geometry (EuroCG 2022) in Perugia [9]. A full version of this paper, which includes appendices but is otherwise identical, is available as a technical report [10].' alternative_title: - LNCS article_processing_charge: No author: - first_name: Phoebe full_name: De Nooijer, Phoebe last_name: De Nooijer - first_name: Soeren full_name: Terziadis, Soeren last_name: Terziadis - first_name: Alexandra full_name: Weinberger, Alexandra last_name: Weinberger - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 - first_name: Tamara full_name: Mchedlidze, Tamara last_name: Mchedlidze - first_name: Maarten full_name: Löffler, Maarten last_name: Löffler - first_name: Günter full_name: Rote, Günter last_name: Rote citation: ama: 'De Nooijer P, Terziadis S, Weinberger A, et al. Removing popular faces in curve arrangements. In: 31st International Symposium on Graph Drawing and Network Visualization. Vol 14466. Springer Nature; 2024:18-33. doi:10.1007/978-3-031-49275-4_2' apa: 'De Nooijer, P., Terziadis, S., Weinberger, A., Masárová, Z., Mchedlidze, T., Löffler, M., & Rote, G. (2024). Removing popular faces in curve arrangements. In 31st International Symposium on Graph Drawing and Network Visualization (Vol. 14466, pp. 18–33). Isola delle Femmine, Palermo, Italy: Springer Nature. https://doi.org/10.1007/978-3-031-49275-4_2' chicago: De Nooijer, Phoebe, Soeren Terziadis, Alexandra Weinberger, Zuzana Masárová, Tamara Mchedlidze, Maarten Löffler, and Günter Rote. “Removing Popular Faces in Curve Arrangements.” In 31st International Symposium on Graph Drawing and Network Visualization, 14466:18–33. Springer Nature, 2024. https://doi.org/10.1007/978-3-031-49275-4_2. ieee: P. De Nooijer et al., “Removing popular faces in curve arrangements,” in 31st International Symposium on Graph Drawing and Network Visualization, Isola delle Femmine, Palermo, Italy, 2024, vol. 14466, pp. 18–33. ista: 'De Nooijer P, Terziadis S, Weinberger A, Masárová Z, Mchedlidze T, Löffler M, Rote G. 2024. Removing popular faces in curve arrangements. 31st International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LNCS, vol. 14466, 18–33.' mla: De Nooijer, Phoebe, et al. “Removing Popular Faces in Curve Arrangements.” 31st International Symposium on Graph Drawing and Network Visualization, vol. 14466, Springer Nature, 2024, pp. 18–33, doi:10.1007/978-3-031-49275-4_2. short: P. De Nooijer, S. Terziadis, A. Weinberger, Z. Masárová, T. Mchedlidze, M. Löffler, G. Rote, in:, 31st International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2024, pp. 18–33. conference: end_date: 2023-09-22 location: Isola delle Femmine, Palermo, Italy name: 'GD: Graph Drawing and Network Visualization' start_date: 2023-09-20 date_created: 2024-01-28T23:01:43Z date_published: 2024-01-06T00:00:00Z date_updated: 2024-01-29T09:45:06Z day: '06' department: - _id: UlWa - _id: HeEd doi: 10.1007/978-3-031-49275-4_2 external_id: arxiv: - '2202.12175' intvolume: ' 14466' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2202.12175 month: '01' oa: 1 oa_version: Preprint page: 18-33 publication: 31st International Symposium on Graph Drawing and Network Visualization publication_identifier: eissn: - 1611-3349 isbn: - '9783031492747' issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Removing popular faces in curve arrangements type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 14466 year: '2024' ... --- _id: '12563' abstract: - lang: eng text: 'he approximate graph coloring problem, whose complexity is unresolved in most cases, concerns finding a c-coloring of a graph that is promised to be k-colorable, where c≥k. This problem naturally generalizes to promise graph homomorphism problems and further to promise constraint satisfaction problems. The complexity of these problems has recently been studied through an algebraic approach. In this paper, we introduce two new techniques to analyze the complexity of promise CSPs: one is based on topology and the other on adjunction. We apply these techniques, together with the previously introduced algebraic approach, to obtain new unconditional NP-hardness results for a significant class of approximate graph coloring and promise graph homomorphism problems.' acknowledgement: "Andrei Krokhin and Jakub Opršal were supported by the UK EPSRC grant EP/R034516/1. Jakub Opršal has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No 101034413. Stanislav Živný was supported by a Royal Society University Research Fellowship. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 714532). The paper re\x1Eects only the authors’ views and not the views of the ERC or the European Commission. " article_processing_charge: No article_type: original author: - first_name: Andrei full_name: Krokhin, Andrei last_name: Krokhin - first_name: Jakub full_name: Opršal, Jakub id: ec596741-c539-11ec-b829-c79322a91242 last_name: Opršal orcid: 0000-0003-1245-3456 - first_name: Marcin full_name: Wrochna, Marcin last_name: Wrochna - first_name: Stanislav full_name: Živný, Stanislav last_name: Živný citation: ama: Krokhin A, Opršal J, Wrochna M, Živný S. Topology and adjunction in promise constraint satisfaction. SIAM Journal on Computing. 2023;52(1):38-79. doi:10.1137/20m1378223 apa: Krokhin, A., Opršal, J., Wrochna, M., & Živný, S. (2023). Topology and adjunction in promise constraint satisfaction. SIAM Journal on Computing. Society for Industrial & Applied Mathematics. https://doi.org/10.1137/20m1378223 chicago: Krokhin, Andrei, Jakub Opršal, Marcin Wrochna, and Stanislav Živný. “Topology and Adjunction in Promise Constraint Satisfaction.” SIAM Journal on Computing. Society for Industrial & Applied Mathematics, 2023. https://doi.org/10.1137/20m1378223. ieee: A. Krokhin, J. Opršal, M. Wrochna, and S. Živný, “Topology and adjunction in promise constraint satisfaction,” SIAM Journal on Computing, vol. 52, no. 1. Society for Industrial & Applied Mathematics, pp. 38–79, 2023. ista: Krokhin A, Opršal J, Wrochna M, Živný S. 2023. Topology and adjunction in promise constraint satisfaction. SIAM Journal on Computing. 52(1), 38–79. mla: Krokhin, Andrei, et al. “Topology and Adjunction in Promise Constraint Satisfaction.” SIAM Journal on Computing, vol. 52, no. 1, Society for Industrial & Applied Mathematics, 2023, pp. 38–79, doi:10.1137/20m1378223. short: A. Krokhin, J. Opršal, M. Wrochna, S. Živný, SIAM Journal on Computing 52 (2023) 38–79. date_created: 2023-02-16T07:03:52Z date_published: 2023-01-01T00:00:00Z date_updated: 2023-08-01T13:11:30Z day: '01' department: - _id: UlWa doi: 10.1137/20m1378223 ec_funded: 1 external_id: arxiv: - '2003.11351' isi: - '000955000000001' intvolume: ' 52' isi: 1 issue: '1' keyword: - General Mathematics - General Computer Science language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2003.11351 month: '01' oa: 1 oa_version: Preprint page: 38-79 project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: Society for Industrial & Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: Topology and adjunction in promise constraint satisfaction type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 52 year: '2023' ... --- _id: '9652' abstract: - lang: eng text: In 1998 Burago and Kleiner and (independently) McMullen gave examples of separated nets in Euclidean space which are non-bilipschitz equivalent to the integer lattice. We study weaker notions of equivalence of separated nets and demonstrate that such notions also give rise to distinct equivalence classes. Put differently, we find occurrences of particularly strong divergence of separated nets from the integer lattice. Our approach generalises that of Burago and Kleiner and McMullen which takes place largely in a continuous setting. Existence of irregular separated nets is verified via the existence of non-realisable density functions ρ:[0,1]d→(0,∞). In the present work we obtain stronger types of non-realisable densities. acknowledgement: 'This work was done while both authors were employed at the University of Innsbruck and enjoyed the full support of Austrian Science Fund (FWF): P 30902-N35.' article_processing_charge: No article_type: original author: - first_name: Michael full_name: Dymond, Michael last_name: Dymond - first_name: Vojtech full_name: Kaluza, Vojtech id: 21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E last_name: Kaluza orcid: 0000-0002-2512-8698 citation: ama: Dymond M, Kaluza V. Highly irregular separated nets. Israel Journal of Mathematics. 2023;253:501-554. doi:10.1007/s11856-022-2448-6 apa: Dymond, M., & Kaluza, V. (2023). Highly irregular separated nets. Israel Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s11856-022-2448-6 chicago: Dymond, Michael, and Vojtech Kaluza. “Highly Irregular Separated Nets.” Israel Journal of Mathematics. Springer Nature, 2023. https://doi.org/10.1007/s11856-022-2448-6. ieee: M. Dymond and V. Kaluza, “Highly irregular separated nets,” Israel Journal of Mathematics, vol. 253. Springer Nature, pp. 501–554, 2023. ista: Dymond M, Kaluza V. 2023. Highly irregular separated nets. Israel Journal of Mathematics. 253, 501–554. mla: Dymond, Michael, and Vojtech Kaluza. “Highly Irregular Separated Nets.” Israel Journal of Mathematics, vol. 253, Springer Nature, 2023, pp. 501–54, doi:10.1007/s11856-022-2448-6. short: M. Dymond, V. Kaluza, Israel Journal of Mathematics 253 (2023) 501–554. date_created: 2021-07-14T07:01:28Z date_published: 2023-03-01T00:00:00Z date_updated: 2023-08-14T11:26:34Z day: '01' ddc: - '515' - '516' department: - _id: UlWa doi: 10.1007/s11856-022-2448-6 external_id: arxiv: - '1903.05923' isi: - '000904950300003' file: - access_level: open_access checksum: 6fa0a3207dd1d6467c309fd1bcc867d1 content_type: application/pdf creator: vkaluza date_created: 2021-07-14T07:41:50Z date_updated: 2021-07-14T07:41:50Z file_id: '9653' file_name: separated_nets.pdf file_size: 900422 relation: main_file file_date_updated: 2021-07-14T07:41:50Z has_accepted_license: '1' intvolume: ' 253' isi: 1 keyword: - Lipschitz - bilipschitz - bounded displacement - modulus of continuity - separated net - non-realisable density - Burago--Kleiner construction language: - iso: eng month: '03' oa: 1 oa_version: Submitted Version page: 501-554 publication: Israel Journal of Mathematics publication_identifier: eissn: - 1565-8511 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Highly irregular separated nets type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 253 year: '2023' ... --- _id: '11999' abstract: - lang: eng text: 'A simple drawing D(G) of a graph G is one where each pair of edges share at most one point: either a common endpoint or a proper crossing. An edge e in the complement of G can be inserted into D(G) if there exists a simple drawing of G+e extending D(G). As a result of Levi’s Enlargement Lemma, if a drawing is rectilinear (pseudolinear), that is, the edges can be extended into an arrangement of lines (pseudolines), then any edge in the complement of G can be inserted. In contrast, we show that it is NP-complete to decide whether one edge can be inserted into a simple drawing. This remains true even if we assume that the drawing is pseudocircular, that is, the edges can be extended to an arrangement of pseudocircles. On the positive side, we show that, given an arrangement of pseudocircles A and a pseudosegment σ, it can be decided in polynomial time whether there exists a pseudocircle Φσ extending σ for which A∪{Φσ} is again an arrangement of pseudocircles.' acknowledgement: 'This work was started during the 6th Austrian–Japanese–Mexican–Spanish Workshop on Discrete Geometry in June 2019 in Austria. We thank all the participants for the good atmosphere as well as discussions on the topic. Also, we thank Jan Kynčl for sending us remarks on a preliminary version of this work and an anonymous referee for further helpful comments.Alan Arroyo was funded by the Marie Skłodowska-Curie grant agreement No 754411. Fabian Klute was partially supported by the Netherlands Organisation for Scientific Research (NWO) under project no. 612.001.651 and by the Austrian Science Fund (FWF): J-4510. Irene Parada and Birgit Vogtenhuber were partially supported by the Austrian Science Fund (FWF): W1230 and within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. Irene Parada was also partially supported by the Independent Research Fund Denmark grant 2020-2023 (9131-00044B) Dynamic Network Analysis and by the Margarita Salas Fellowship funded by the Ministry of Universities of Spain and the European Union (NextGenerationEU). Tilo Wiedera was supported by the German Research Foundation (DFG) grant CH 897/2-2.' article_processing_charge: Yes (in subscription journal) article_type: original author: - first_name: Alan M full_name: Arroyo Guevara, Alan M id: 3207FDC6-F248-11E8-B48F-1D18A9856A87 last_name: Arroyo Guevara orcid: 0000-0003-2401-8670 - first_name: Fabian full_name: Klute, Fabian last_name: Klute - first_name: Irene full_name: Parada, Irene last_name: Parada - first_name: Birgit full_name: Vogtenhuber, Birgit last_name: Vogtenhuber - first_name: Raimund full_name: Seidel, Raimund last_name: Seidel - first_name: Tilo full_name: Wiedera, Tilo last_name: Wiedera citation: ama: Arroyo Guevara AM, Klute F, Parada I, Vogtenhuber B, Seidel R, Wiedera T. Inserting one edge into a simple drawing is hard. Discrete and Computational Geometry. 2023;69:745–770. doi:10.1007/s00454-022-00394-9 apa: Arroyo Guevara, A. M., Klute, F., Parada, I., Vogtenhuber, B., Seidel, R., & Wiedera, T. (2023). Inserting one edge into a simple drawing is hard. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00394-9 chicago: Arroyo Guevara, Alan M, Fabian Klute, Irene Parada, Birgit Vogtenhuber, Raimund Seidel, and Tilo Wiedera. “Inserting One Edge into a Simple Drawing Is Hard.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-022-00394-9. ieee: A. M. Arroyo Guevara, F. Klute, I. Parada, B. Vogtenhuber, R. Seidel, and T. Wiedera, “Inserting one edge into a simple drawing is hard,” Discrete and Computational Geometry, vol. 69. Springer Nature, pp. 745–770, 2023. ista: Arroyo Guevara AM, Klute F, Parada I, Vogtenhuber B, Seidel R, Wiedera T. 2023. Inserting one edge into a simple drawing is hard. Discrete and Computational Geometry. 69, 745–770. mla: Arroyo Guevara, Alan M., et al. “Inserting One Edge into a Simple Drawing Is Hard.” Discrete and Computational Geometry, vol. 69, Springer Nature, 2023, pp. 745–770, doi:10.1007/s00454-022-00394-9. short: A.M. Arroyo Guevara, F. Klute, I. Parada, B. Vogtenhuber, R. Seidel, T. Wiedera, Discrete and Computational Geometry 69 (2023) 745–770. date_created: 2022-08-28T22:02:01Z date_published: 2023-04-01T00:00:00Z date_updated: 2023-08-14T12:51:25Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.1007/s00454-022-00394-9 ec_funded: 1 external_id: arxiv: - '1909.07347' isi: - '000840292800001' file: - access_level: open_access checksum: def7ae3b28d9fd6aec16450e40090302 content_type: application/pdf creator: alisjak date_created: 2022-08-29T11:23:15Z date_updated: 2022-08-29T11:23:15Z file_id: '12006' file_name: 2022_DiscreteandComputionalGeometry_Arroyo.pdf file_size: 1002218 relation: main_file success: 1 file_date_updated: 2022-08-29T11:23:15Z has_accepted_license: '1' intvolume: ' 69' isi: 1 language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '04' oa: 1 oa_version: Published Version page: 745–770 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Discrete and Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Inserting one edge into a simple drawing is hard tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 69 year: '2023' ... --- _id: '13969' abstract: - lang: eng text: "Bundling crossings is a strategy which can enhance the readability\r\nof graph drawings. In this paper we consider good drawings, i.e., we require that\r\nany two edges have at most one common point which can be a common vertex or a\r\ncrossing. Our main result is that there is a polynomial-time algorithm to compute an\r\n8-approximation of the bundled crossing number of a good drawing with no toothed\r\nhole. In general the number of toothed holes has to be added to the 8-approximation.\r\nIn the special case of circular drawings the approximation factor is 8, this improves\r\nupon the 10-approximation of Fink et al. [14]. Our approach also works with the same\r\napproximation factor for families of pseudosegments, i.e., curves intersecting at most\r\nonce. We also show how to compute a 9/2-approximation when the intersection graph of\r\nthe pseudosegments is bipartite and has no toothed hole." acknowledgement: This work was initiated during the Workshop on Geometric Graphs in November 2019 in Strobl, Austria. We would like to thank Oswin Aichholzer, Fabian Klute, Man-Kwun Chiu, Martin Balko, Pavel Valtr for their avid discussions during the workshop. The first author has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No 754411. The second author has been supported by the German Research Foundation DFG Project FE 340/12-1. An extended abstract of this paper has been published in the proceedings of WALCOM 2022 in the Springer LNCS series, vol. 13174, pages 383–395. article_processing_charge: Yes article_type: original author: - first_name: Alan M full_name: Arroyo Guevara, Alan M id: 3207FDC6-F248-11E8-B48F-1D18A9856A87 last_name: Arroyo Guevara orcid: 0000-0003-2401-8670 - first_name: Stefan full_name: Felsner, Stefan last_name: Felsner citation: ama: Arroyo Guevara AM, Felsner S. Approximating the bundled crossing number. Journal of Graph Algorithms and Applications. 2023;27(6):433-457. doi:10.7155/jgaa.00629 apa: Arroyo Guevara, A. M., & Felsner, S. (2023). Approximating the bundled crossing number. Journal of Graph Algorithms and Applications. Brown University. https://doi.org/10.7155/jgaa.00629 chicago: Arroyo Guevara, Alan M, and Stefan Felsner. “Approximating the Bundled Crossing Number.” Journal of Graph Algorithms and Applications. Brown University, 2023. https://doi.org/10.7155/jgaa.00629. ieee: A. M. Arroyo Guevara and S. Felsner, “Approximating the bundled crossing number,” Journal of Graph Algorithms and Applications, vol. 27, no. 6. Brown University, pp. 433–457, 2023. ista: Arroyo Guevara AM, Felsner S. 2023. Approximating the bundled crossing number. Journal of Graph Algorithms and Applications. 27(6), 433–457. mla: Arroyo Guevara, Alan M., and Stefan Felsner. “Approximating the Bundled Crossing Number.” Journal of Graph Algorithms and Applications, vol. 27, no. 6, Brown University, 2023, pp. 433–57, doi:10.7155/jgaa.00629. short: A.M. Arroyo Guevara, S. Felsner, Journal of Graph Algorithms and Applications 27 (2023) 433–457. date_created: 2023-08-06T22:01:11Z date_published: 2023-07-01T00:00:00Z date_updated: 2023-09-25T10:56:10Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.7155/jgaa.00629 ec_funded: 1 external_id: arxiv: - '2109.14892' file: - access_level: open_access checksum: 9c30d2b8e324cc1c904f2aeec92013a3 content_type: application/pdf creator: dernst date_created: 2023-08-07T08:00:48Z date_updated: 2023-08-07T08:00:48Z file_id: '13979' file_name: 2023_JourGraphAlgorithms_Arroyo.pdf file_size: 865774 relation: main_file success: 1 file_date_updated: 2023-08-07T08:00:48Z has_accepted_license: '1' intvolume: ' 27' issue: '6' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 433-457 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Journal of Graph Algorithms and Applications publication_identifier: issn: - 1526-1719 publication_status: published publisher: Brown University quality_controlled: '1' related_material: record: - id: '11185' relation: earlier_version status: public scopus_import: '1' status: public title: Approximating the bundled crossing number tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 27 year: '2023' ... --- _id: '13331' abstract: - lang: eng text: "The extension of extremal combinatorics to the setting of exterior algebra is a work\r\nin progress that gained attention recently. In this thesis, we study the combinatorial structure of exterior algebra by introducing a dictionary that translates the notions from the set systems into the framework of exterior algebra. We show both generalizations of celebrated Erdös--Ko--Rado theorem and Hilton--Milner theorem to the setting of exterior algebra in the simplest non-trivial case of two-forms.\r\n" alternative_title: - ISTA Master's Thesis article_processing_charge: No author: - first_name: Seyda full_name: Köse, Seyda id: 8ba3170d-dc85-11ea-9058-c4251c96a6eb last_name: Köse citation: ama: Köse S. Exterior algebra and combinatorics. 2023. doi:10.15479/at:ista:13331 apa: Köse, S. (2023). Exterior algebra and combinatorics. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:13331 chicago: Köse, Seyda. “Exterior Algebra and Combinatorics.” Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:13331. ieee: S. Köse, “Exterior algebra and combinatorics,” Institute of Science and Technology Austria, 2023. ista: Köse S. 2023. Exterior algebra and combinatorics. Institute of Science and Technology Austria. mla: Köse, Seyda. Exterior Algebra and Combinatorics. Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:13331. short: S. Köse, Exterior Algebra and Combinatorics, Institute of Science and Technology Austria, 2023. date_created: 2023-07-31T10:20:55Z date_published: 2023-07-31T00:00:00Z date_updated: 2023-10-04T11:54:56Z day: '31' ddc: - '510' - '516' degree_awarded: MS department: - _id: GradSch - _id: UlWa doi: 10.15479/at:ista:13331 file: - access_level: closed checksum: 96ee518d796d02af71395622c45de03c content_type: application/x-zip-compressed creator: skoese date_created: 2023-07-31T10:16:32Z date_updated: 2023-07-31T10:16:32Z file_id: '13333' file_name: Exterior Algebra and Combinatorics.zip file_size: 28684 relation: source_file - access_level: open_access checksum: f610f4713f88bc477de576aaa46b114e content_type: application/pdf creator: skoese date_created: 2023-08-03T15:28:55Z date_updated: 2023-08-03T15:28:55Z file_id: '13480' file_name: thesis-pdfa.pdf file_size: 4953418 relation: main_file success: 1 file_date_updated: 2023-08-03T15:28:55Z has_accepted_license: '1' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: '26' publication_identifier: issn: - 2791-4585 publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '12680' relation: part_of_dissertation status: public status: public supervisor: - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 title: Exterior algebra and combinatorics type: dissertation user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2023' ... --- _id: '12680' abstract: - lang: eng text: The celebrated Erdős–Ko–Rado theorem about the maximal size of an intersecting family of r-element subsets of was extended to the setting of exterior algebra in [5, Theorem 2.3] and in [6, Theorem 1.4]. However, the equality case has not been settled yet. In this short note, we show that the extension of the Erdős–Ko–Rado theorem and the characterization of the equality case therein, as well as those of the Hilton–Milner theorem to the setting of exterior algebra in the simplest non-trivial case of two-forms follow from a folklore puzzle about possible arrangements of an intersecting family of lines. article_number: '113363' article_processing_charge: No article_type: letter_note author: - first_name: Grigory full_name: Ivanov, Grigory id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E last_name: Ivanov - first_name: Seyda full_name: Köse, Seyda id: 8ba3170d-dc85-11ea-9058-c4251c96a6eb last_name: Köse citation: ama: Ivanov G, Köse S. Erdős-Ko-Rado and Hilton-Milner theorems for two-forms. Discrete Mathematics. 2023;346(6). doi:10.1016/j.disc.2023.113363 apa: Ivanov, G., & Köse, S. (2023). Erdős-Ko-Rado and Hilton-Milner theorems for two-forms. Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.disc.2023.113363 chicago: Ivanov, Grigory, and Seyda Köse. “Erdős-Ko-Rado and Hilton-Milner Theorems for Two-Forms.” Discrete Mathematics. Elsevier, 2023. https://doi.org/10.1016/j.disc.2023.113363. ieee: G. Ivanov and S. Köse, “Erdős-Ko-Rado and Hilton-Milner theorems for two-forms,” Discrete Mathematics, vol. 346, no. 6. Elsevier, 2023. ista: Ivanov G, Köse S. 2023. Erdős-Ko-Rado and Hilton-Milner theorems for two-forms. Discrete Mathematics. 346(6), 113363. mla: Ivanov, Grigory, and Seyda Köse. “Erdős-Ko-Rado and Hilton-Milner Theorems for Two-Forms.” Discrete Mathematics, vol. 346, no. 6, 113363, Elsevier, 2023, doi:10.1016/j.disc.2023.113363. short: G. Ivanov, S. Köse, Discrete Mathematics 346 (2023). date_created: 2023-02-26T23:01:00Z date_published: 2023-06-01T00:00:00Z date_updated: 2023-10-04T11:54:57Z day: '01' department: - _id: UlWa - _id: GradSch doi: 10.1016/j.disc.2023.113363 external_id: arxiv: - '2201.10892' intvolume: ' 346' issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.2201.10892' month: '06' oa: 1 oa_version: Preprint publication: Discrete Mathematics publication_identifier: issn: - 0012-365X publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '13331' relation: dissertation_contains status: public scopus_import: '1' status: public title: Erdős-Ko-Rado and Hilton-Milner theorems for two-forms type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 346 year: '2023' ... --- _id: '14660' abstract: - lang: eng text: "The classical Steinitz theorem states that if the origin belongs to the interior of the convex hull of a set \U0001D446⊂ℝ\U0001D451, then there are at most 2\U0001D451 points of \U0001D446 whose convex hull contains the origin in the interior. Bárány, Katchalski,and Pach proved the following quantitative version of Steinitz’s theorem. Let \U0001D444 be a convex polytope in ℝ\U0001D451 containing the standard Euclidean unit ball \U0001D401\U0001D451. Then there exist at most 2\U0001D451 vertices of \U0001D444 whose convex hull \U0001D444′ satisfies \U0001D45F\U0001D401\U0001D451⊂\U0001D444′ with \U0001D45F⩾\U0001D451−2\U0001D451. They conjectured that \U0001D45F⩾\U0001D450\U0001D451−1∕2 holds with a universal constant \U0001D450>0. We prove \U0001D45F⩾15\U0001D4512, the first polynomial lower bound on \U0001D45F. Furthermore, we show that \U0001D45F is not greater than 2/√\U0001D451." acknowledgement: M.N. was supported by the János Bolyai Scholarship of the Hungarian Academy of Sciences aswell as the National Research, Development and Innovation Fund (NRDI) grants K119670 andK131529, and the ÚNKP-22-5 New National Excellence Program of the Ministry for Innovationand Technology from the source of the NRDI as well as the ELTE TKP 2021-NKTA-62 fundingscheme article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Grigory full_name: Ivanov, Grigory id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E last_name: Ivanov - first_name: Márton full_name: Naszódi, Márton last_name: Naszódi citation: ama: 'Ivanov G, Naszódi M. Quantitative Steinitz theorem: A polynomial bound. Bulletin of the London Mathematical Society. 2023. doi:10.1112/blms.12965' apa: 'Ivanov, G., & Naszódi, M. (2023). Quantitative Steinitz theorem: A polynomial bound. Bulletin of the London Mathematical Society. London Mathematical Society. https://doi.org/10.1112/blms.12965' chicago: 'Ivanov, Grigory, and Márton Naszódi. “Quantitative Steinitz Theorem: A Polynomial Bound.” Bulletin of the London Mathematical Society. London Mathematical Society, 2023. https://doi.org/10.1112/blms.12965.' ieee: 'G. Ivanov and M. Naszódi, “Quantitative Steinitz theorem: A polynomial bound,” Bulletin of the London Mathematical Society. London Mathematical Society, 2023.' ista: 'Ivanov G, Naszódi M. 2023. Quantitative Steinitz theorem: A polynomial bound. Bulletin of the London Mathematical Society.' mla: 'Ivanov, Grigory, and Márton Naszódi. “Quantitative Steinitz Theorem: A Polynomial Bound.” Bulletin of the London Mathematical Society, London Mathematical Society, 2023, doi:10.1112/blms.12965.' short: G. Ivanov, M. Naszódi, Bulletin of the London Mathematical Society (2023). date_created: 2023-12-10T23:00:58Z date_published: 2023-12-04T00:00:00Z date_updated: 2023-12-11T10:03:54Z day: '04' department: - _id: UlWa doi: 10.1112/blms.12965 external_id: arxiv: - '2212.04308' language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.1112/blms.12965' month: '12' oa: 1 oa_version: Published Version publication: Bulletin of the London Mathematical Society publication_identifier: eissn: - 1469-2120 issn: - 0024-6093 publication_status: epub_ahead publisher: London Mathematical Society quality_controlled: '1' scopus_import: '1' status: public title: 'Quantitative Steinitz theorem: A polynomial bound' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '13974' abstract: - lang: eng text: The Tverberg theorem is one of the cornerstones of discrete geometry. It states that, given a set X of at least (d+1)(r−1)+1 points in Rd, one can find a partition X=X1∪⋯∪Xr of X, such that the convex hulls of the Xi, i=1,…,r, all share a common point. In this paper, we prove a trengthening of this theorem that guarantees a partition which, in addition to the above, has the property that the boundaries of full-dimensional convex hulls have pairwise nonempty intersections. Possible generalizations and algorithmic aspects are also discussed. As a concrete application, we show that any n points in the plane in general position span ⌊n/3⌋ vertex-disjoint triangles that are pairwise crossing, meaning that their boundaries have pairwise nonempty intersections; this number is clearly best possible. A previous result of Álvarez-Rebollar et al. guarantees ⌊n/6⌋pairwise crossing triangles. Our result generalizes to a result about simplices in Rd, d≥2. acknowledgement: "Part of the research leading to this paper was done during the 16th Gremo Workshop on Open Problems (GWOP), Waltensburg, Switzerland, June 12–16, 2018. We thank Patrick Schnider for suggesting the problem, and Stefan Felsner, Malte Milatz, and Emo Welzl for fruitful discussions during the workshop. We also thank Stefan Felsner and Manfred Scheucher for finding, communicating the example from Sect. 3.3, and the kind permission to include their visualization of the point set. We thank Dömötör Pálvölgyi, the SoCG reviewers, and DCG reviewers for various helpful comments.\r\nR. Fulek gratefully acknowledges support from Austrian Science Fund (FWF), Project M2281-N35. A. Kupavskii was supported by the Advanced Postdoc.Mobility Grant no. P300P2_177839 of the Swiss National Science Foundation. Research by P. Valtr was supported by the Grant no. 18-19158 S of the Czech Science Foundation (GAČR)." article_processing_charge: No article_type: original author: - first_name: Radoslav full_name: Fulek, Radoslav id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87 last_name: Fulek orcid: 0000-0001-8485-1774 - first_name: Bernd full_name: Gärtner, Bernd last_name: Gärtner - first_name: Andrey full_name: Kupavskii, Andrey last_name: Kupavskii - first_name: Pavel full_name: Valtr, Pavel last_name: Valtr - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: Fulek R, Gärtner B, Kupavskii A, Valtr P, Wagner U. The crossing Tverberg theorem. Discrete and Computational Geometry. 2023. doi:10.1007/s00454-023-00532-x apa: Fulek, R., Gärtner, B., Kupavskii, A., Valtr, P., & Wagner, U. (2023). The crossing Tverberg theorem. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00532-x chicago: Fulek, Radoslav, Bernd Gärtner, Andrey Kupavskii, Pavel Valtr, and Uli Wagner. “The Crossing Tverberg Theorem.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-023-00532-x. ieee: R. Fulek, B. Gärtner, A. Kupavskii, P. Valtr, and U. Wagner, “The crossing Tverberg theorem,” Discrete and Computational Geometry. Springer Nature, 2023. ista: Fulek R, Gärtner B, Kupavskii A, Valtr P, Wagner U. 2023. The crossing Tverberg theorem. Discrete and Computational Geometry. mla: Fulek, Radoslav, et al. “The Crossing Tverberg Theorem.” Discrete and Computational Geometry, Springer Nature, 2023, doi:10.1007/s00454-023-00532-x. short: R. Fulek, B. Gärtner, A. Kupavskii, P. Valtr, U. Wagner, Discrete and Computational Geometry (2023). date_created: 2023-08-06T22:01:12Z date_published: 2023-07-27T00:00:00Z date_updated: 2023-12-13T12:03:35Z day: '27' department: - _id: UlWa doi: 10.1007/s00454-023-00532-x external_id: arxiv: - '1812.04911' isi: - '001038546500001' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.1812.04911 month: '07' oa: 1 oa_version: Preprint project: - _id: 261FA626-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02281 name: Eliminating intersections in drawings of graphs publication: Discrete and Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '6647' relation: earlier_version status: public scopus_import: '1' status: public title: The crossing Tverberg theorem type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '14445' abstract: - lang: eng text: "We prove the following quantitative Borsuk–Ulam-type result (an equivariant analogue of Gromov’s Topological Overlap Theorem): Let X be a free ℤ/2-complex of dimension d with coboundary expansion at least ηk in dimension 0 ≤ k < d. Then for every equivariant map F: X →ℤ/2 ℝd, the fraction of d-simplices σ of X with 0 ∈ F (σ) is at least 2−d Π d−1k=0ηk.\r\n\r\nAs an application, we show that for every sufficiently thick d-dimensional spherical building Y and every map f: Y → ℝ2d, we have f(σ) ∩ f(τ) ≠ ∅ for a constant fraction μd > 0 of pairs {σ, τ} of d-simplices of Y. In particular, such complexes are non-embeddable into ℝ2d, which proves a conjecture of Tancer and Vorwerk for sufficiently thick spherical buildings.\r\n\r\nWe complement these results by upper bounds on the coboundary expansion of two families of simplicial complexes; this indicates some limitations to the bounds one can obtain by straighforward applications of the quantitative Borsuk–Ulam theorem. Specifically, we prove\r\n\r\n• an upper bound of (d + 1)/2d on the normalized (d − 1)-th coboundary expansion constant of complete (d + 1)-partite d-dimensional complexes (under a mild divisibility assumption on the sizes of the parts); and\r\n\r\n• an upper bound of (d + 1)/2d + ε on the normalized (d − 1)-th coboundary expansion of the d-dimensional spherical building associated with GLd+2(Fq) for any ε > 0 and sufficiently large q. This disproves, in a rather strong sense, a conjecture of Lubotzky, Meshulam and Mozes." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 - first_name: Pascal full_name: Wild, Pascal id: 4C20D868-F248-11E8-B48F-1D18A9856A87 last_name: Wild citation: ama: Wagner U, Wild P. Coboundary expansion, equivariant overlap, and crossing numbers of simplicial complexes. Israel Journal of Mathematics. 2023;256(2):675-717. doi:10.1007/s11856-023-2521-9 apa: Wagner, U., & Wild, P. (2023). Coboundary expansion, equivariant overlap, and crossing numbers of simplicial complexes. Israel Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s11856-023-2521-9 chicago: Wagner, Uli, and Pascal Wild. “Coboundary Expansion, Equivariant Overlap, and Crossing Numbers of Simplicial Complexes.” Israel Journal of Mathematics. Springer Nature, 2023. https://doi.org/10.1007/s11856-023-2521-9. ieee: U. Wagner and P. Wild, “Coboundary expansion, equivariant overlap, and crossing numbers of simplicial complexes,” Israel Journal of Mathematics, vol. 256, no. 2. Springer Nature, pp. 675–717, 2023. ista: Wagner U, Wild P. 2023. Coboundary expansion, equivariant overlap, and crossing numbers of simplicial complexes. Israel Journal of Mathematics. 256(2), 675–717. mla: Wagner, Uli, and Pascal Wild. “Coboundary Expansion, Equivariant Overlap, and Crossing Numbers of Simplicial Complexes.” Israel Journal of Mathematics, vol. 256, no. 2, Springer Nature, 2023, pp. 675–717, doi:10.1007/s11856-023-2521-9. short: U. Wagner, P. Wild, Israel Journal of Mathematics 256 (2023) 675–717. date_created: 2023-10-22T22:01:14Z date_published: 2023-09-01T00:00:00Z date_updated: 2023-12-13T13:09:07Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.1007/s11856-023-2521-9 external_id: isi: - '001081646400010' file: - access_level: open_access checksum: fbb05619fe4b650f341cc730425dd9c3 content_type: application/pdf creator: dernst date_created: 2023-10-31T11:20:31Z date_updated: 2023-10-31T11:20:31Z file_id: '14475' file_name: 2023_IsraelJourMath_Wagner.pdf file_size: 623787 relation: main_file success: 1 file_date_updated: 2023-10-31T11:20:31Z has_accepted_license: '1' intvolume: ' 256' isi: 1 issue: '2' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 675-717 publication: Israel Journal of Mathematics publication_identifier: eissn: - 1565-8511 issn: - 0021-2172 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Coboundary expansion, equivariant overlap, and crossing numbers of simplicial complexes tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 256 year: '2023' ... --- _id: '12833' abstract: - lang: eng text: 'The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results: 1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan. 2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2. 3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved.' acknowledgement: "This work was begun at the University of Waterloo and was partially supported by the Natural Sciences and Engineering Council of Canada (NSERC).\r\n" article_number: '9' article_processing_charge: No article_type: original author: - first_name: Ahmad full_name: Biniaz, Ahmad last_name: Biniaz - first_name: Kshitij full_name: Jain, Kshitij last_name: Jain - first_name: Anna full_name: Lubiw, Anna last_name: Lubiw - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 - first_name: Tillmann full_name: Miltzow, Tillmann last_name: Miltzow - first_name: Debajyoti full_name: Mondal, Debajyoti last_name: Mondal - first_name: Anurag Murty full_name: Naredla, Anurag Murty last_name: Naredla - first_name: Josef full_name: Tkadlec, Josef id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87 last_name: Tkadlec orcid: 0000-0002-1097-9684 - first_name: Alexi full_name: Turcotte, Alexi last_name: Turcotte citation: ama: Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. 2023;24(2). doi:10.46298/DMTCS.8383 apa: Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (2023). Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. EPI Sciences. https://doi.org/10.46298/DMTCS.8383 chicago: Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow, Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token Swapping on Trees.” Discrete Mathematics and Theoretical Computer Science. EPI Sciences, 2023. https://doi.org/10.46298/DMTCS.8383. ieee: A. Biniaz et al., “Token swapping on trees,” Discrete Mathematics and Theoretical Computer Science, vol. 24, no. 2. EPI Sciences, 2023. ista: Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. 2023. Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. 24(2), 9. mla: Biniaz, Ahmad, et al. “Token Swapping on Trees.” Discrete Mathematics and Theoretical Computer Science, vol. 24, no. 2, 9, EPI Sciences, 2023, doi:10.46298/DMTCS.8383. short: A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, Discrete Mathematics and Theoretical Computer Science 24 (2023). date_created: 2023-04-16T22:01:08Z date_published: 2023-01-18T00:00:00Z date_updated: 2024-01-04T12:42:09Z day: '18' ddc: - '000' department: - _id: KrCh - _id: HeEd - _id: UlWa doi: 10.46298/DMTCS.8383 external_id: arxiv: - '1903.06981' file: - access_level: open_access checksum: 439102ea4f6e2aeefd7107dfb9ccf532 content_type: application/pdf creator: dernst date_created: 2023-04-17T08:10:28Z date_updated: 2023-04-17T08:10:28Z file_id: '12844' file_name: 2022_DMTCS_Biniaz.pdf file_size: 2072197 relation: main_file success: 1 file_date_updated: 2023-04-17T08:10:28Z has_accepted_license: '1' intvolume: ' 24' issue: '2' language: - iso: eng month: '01' oa: 1 oa_version: Published Version publication: Discrete Mathematics and Theoretical Computer Science publication_identifier: eissn: - 1365-8050 issn: - 1462-7264 publication_status: published publisher: EPI Sciences quality_controlled: '1' related_material: record: - id: '7950' relation: earlier_version status: public scopus_import: '1' status: public title: Token swapping on trees tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 24 year: '2023' ... --- _id: '14737' abstract: - lang: eng text: 'John’s fundamental theorem characterizing the largest volume ellipsoid contained in a convex body $K$ in $\mathbb{R}^{d}$ has seen several generalizations and extensions. One direction, initiated by V. Milman is to replace ellipsoids by positions (affine images) of another body $L$. Another, more recent direction is to consider logarithmically concave functions on $\mathbb{R}^{d}$ instead of convex bodies: we designate some special, radially symmetric log-concave function $g$ as the analogue of the Euclidean ball, and want to find its largest integral position under the constraint that it is pointwise below some given log-concave function $f$. We follow both directions simultaneously: we consider the functional question, and allow essentially any meaningful function to play the role of $g$ above. Our general theorems jointly extend known results in both directions. The dual problem in the setting of convex bodies asks for the smallest volume ellipsoid, called Löwner’s ellipsoid, containing $K$. We consider the analogous problem for functions: we characterize the solutions of the optimization problem of finding a smallest integral position of some log-concave function $g$ under the constraint that it is pointwise above $f$. It turns out that in the functional setting, the relationship between the John and the Löwner problems is more intricate than it is in the setting of convex bodies.' acknowledgement: "We thank Alexander Litvak for the many discussions on Theorem 1.1. Igor Tsiutsiurupa participated in the early stage of this project. To our deep regret, Igor chose another road for his life and stopped working with us.\r\nThis work was supported by the János Bolyai Scholarship of the Hungarian Academy of Sciences [to M.N.]; the National Research, Development, and Innovation Fund (NRDI) [K119670 and K131529 to M.N.]; and the ÚNKP-22-5 New National Excellence Program of the Ministry for Innovation and Technology from the source of the NRDI [to M.N.]." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Grigory full_name: Ivanov, Grigory id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E last_name: Ivanov - first_name: Márton full_name: Naszódi, Márton last_name: Naszódi citation: ama: Ivanov G, Naszódi M. Functional John and Löwner conditions for pairs of log-concave functions. International Mathematics Research Notices. 2023;2023(23):20613-20669. doi:10.1093/imrn/rnad210 apa: Ivanov, G., & Naszódi, M. (2023). Functional John and Löwner conditions for pairs of log-concave functions. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnad210 chicago: Ivanov, Grigory, and Márton Naszódi. “Functional John and Löwner Conditions for Pairs of Log-Concave Functions.” International Mathematics Research Notices. Oxford University Press, 2023. https://doi.org/10.1093/imrn/rnad210. ieee: G. Ivanov and M. Naszódi, “Functional John and Löwner conditions for pairs of log-concave functions,” International Mathematics Research Notices, vol. 2023, no. 23. Oxford University Press, pp. 20613–20669, 2023. ista: Ivanov G, Naszódi M. 2023. Functional John and Löwner conditions for pairs of log-concave functions. International Mathematics Research Notices. 2023(23), 20613–20669. mla: Ivanov, Grigory, and Márton Naszódi. “Functional John and Löwner Conditions for Pairs of Log-Concave Functions.” International Mathematics Research Notices, vol. 2023, no. 23, Oxford University Press, 2023, pp. 20613–69, doi:10.1093/imrn/rnad210. short: G. Ivanov, M. Naszódi, International Mathematics Research Notices 2023 (2023) 20613–20669. date_created: 2024-01-08T09:48:56Z date_published: 2023-12-01T00:00:00Z date_updated: 2024-01-08T09:57:25Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.1093/imrn/rnad210 external_id: arxiv: - '2212.11781' file: - access_level: open_access checksum: 353666cea80633beb0f1ffd342dff6d4 content_type: application/pdf creator: dernst date_created: 2024-01-08T09:53:09Z date_updated: 2024-01-08T09:53:09Z file_id: '14738' file_name: 2023_IMRN_Ivanov.pdf file_size: 815777 relation: main_file success: 1 file_date_updated: 2024-01-08T09:53:09Z has_accepted_license: '1' intvolume: ' 2023' issue: '23' keyword: - General Mathematics language: - iso: eng license: https://creativecommons.org/licenses/by-nc-nd/4.0/ month: '12' oa: 1 oa_version: Published Version page: 20613-20669 publication: International Mathematics Research Notices publication_identifier: eissn: - 1687-0247 issn: - 1073-7928 publication_status: published publisher: Oxford University Press quality_controlled: '1' status: public title: Functional John and Löwner conditions for pairs of log-concave functions tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 2023 year: '2023' ... --- _id: '9651' abstract: - lang: eng text: We introduce a hierachy of equivalence relations on the set of separated nets of a given Euclidean space, indexed by concave increasing functions ϕ:(0,∞)→(0,∞). Two separated nets are called ϕ-displacement equivalent if, roughly speaking, there is a bijection between them which, for large radii R, displaces points of norm at most R by something of order at most ϕ(R). We show that the spectrum of ϕ-displacement equivalence spans from the established notion of bounded displacement equivalence, which corresponds to bounded ϕ, to the indiscrete equivalence relation, coresponding to ϕ(R)∈Ω(R), in which all separated nets are equivalent. In between the two ends of this spectrum, the notions of ϕ-displacement equivalence are shown to be pairwise distinct with respect to the asymptotic classes of ϕ(R) for R→∞. We further undertake a comparison of our notion of ϕ-displacement equivalence with previously studied relations on separated nets. Particular attention is given to the interaction of the notions of ϕ-displacement equivalence with that of bilipschitz equivalence. acknowledgement: 'Open access funding provided by Institute of Science and Technology (IST Austria). This work was started while both authors were employed at the University of Innsbruck and enjoyed the full support of Austrian Science Fund (FWF): P 30902-N35. It was continued when the first named author was employed at University of Leipzig and the second named author was employed at Institute of Science and Technology of Austria, where he was supported by an IST Fellowship.' article_number: '15' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Michael full_name: Dymond, Michael last_name: Dymond - first_name: Vojtech full_name: Kaluza, Vojtech id: 21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E last_name: Kaluza orcid: 0000-0002-2512-8698 citation: ama: Dymond M, Kaluza V. Divergence of separated nets with respect to displacement equivalence. Geometriae Dedicata. 2023. doi:10.1007/s10711-023-00862-3 apa: Dymond, M., & Kaluza, V. (2023). Divergence of separated nets with respect to displacement equivalence. Geometriae Dedicata. Springer Nature. https://doi.org/10.1007/s10711-023-00862-3 chicago: Dymond, Michael, and Vojtech Kaluza. “Divergence of Separated Nets with Respect to Displacement Equivalence.” Geometriae Dedicata. Springer Nature, 2023. https://doi.org/10.1007/s10711-023-00862-3. ieee: M. Dymond and V. Kaluza, “Divergence of separated nets with respect to displacement equivalence,” Geometriae Dedicata. Springer Nature, 2023. ista: Dymond M, Kaluza V. 2023. Divergence of separated nets with respect to displacement equivalence. Geometriae Dedicata., 15. mla: Dymond, Michael, and Vojtech Kaluza. “Divergence of Separated Nets with Respect to Displacement Equivalence.” Geometriae Dedicata, 15, Springer Nature, 2023, doi:10.1007/s10711-023-00862-3. short: M. Dymond, V. Kaluza, Geometriae Dedicata (2023). date_created: 2021-07-14T07:01:27Z date_published: 2023-11-17T00:00:00Z date_updated: 2024-01-11T13:06:32Z day: '17' department: - _id: UlWa doi: 10.1007/s10711-023-00862-3 external_id: arxiv: - '2102.13046' isi: - '001105681500001' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s10711-023-00862-3 month: '11' oa: 1 oa_version: Published Version publication: Geometriae Dedicata publication_identifier: eissn: - 1572-9168 issn: - 0046-5755 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Divergence of separated nets with respect to displacement equivalence type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '13270' abstract: - lang: eng text: "Consider a geodesic triangle on a surface of constant curvature and subdivide it recursively into four triangles by joining the midpoints of its edges. We show the existence of a uniform δ>0\r\n such that, at any step of the subdivision, all the triangle angles lie in the interval (δ,π−δ)\r\n. Additionally, we exhibit stabilising behaviours for both angles and lengths as this subdivision progresses." acknowledgement: Open access funding provided by the Institute of Science and Technology (IST Austria). article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Florestan R full_name: Brunck, Florestan R id: 6ab6e556-f394-11eb-9cf6-9dfb78f00d8d last_name: Brunck citation: ama: Brunck FR. Iterated medial triangle subdivision in surfaces of constant curvature. Discrete and Computational Geometry. 2023;70(3):1059-1089. doi:10.1007/s00454-023-00500-5 apa: Brunck, F. R. (2023). Iterated medial triangle subdivision in surfaces of constant curvature. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00500-5 chicago: Brunck, Florestan R. “Iterated Medial Triangle Subdivision in Surfaces of Constant Curvature.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-023-00500-5. ieee: F. R. Brunck, “Iterated medial triangle subdivision in surfaces of constant curvature,” Discrete and Computational Geometry, vol. 70, no. 3. Springer Nature, pp. 1059–1089, 2023. ista: Brunck FR. 2023. Iterated medial triangle subdivision in surfaces of constant curvature. Discrete and Computational Geometry. 70(3), 1059–1089. mla: Brunck, Florestan R. “Iterated Medial Triangle Subdivision in Surfaces of Constant Curvature.” Discrete and Computational Geometry, vol. 70, no. 3, Springer Nature, 2023, pp. 1059–89, doi:10.1007/s00454-023-00500-5. short: F.R. Brunck, Discrete and Computational Geometry 70 (2023) 1059–1089. date_created: 2023-07-23T22:01:14Z date_published: 2023-07-05T00:00:00Z date_updated: 2024-01-29T11:16:16Z day: '05' ddc: - '510' department: - _id: UlWa doi: 10.1007/s00454-023-00500-5 external_id: arxiv: - '2107.04112' isi: - '001023742800003' file: - access_level: open_access checksum: 865e68daafdd4edcfc280172ec50f5ea content_type: application/pdf creator: dernst date_created: 2024-01-29T11:15:22Z date_updated: 2024-01-29T11:15:22Z file_id: '14897' file_name: 2023_DiscreteComputGeometry_Brunck.pdf file_size: 1466020 relation: main_file success: 1 file_date_updated: 2024-01-29T11:15:22Z has_accepted_license: '1' intvolume: ' 70' isi: 1 issue: '3' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 1059-1089 publication: Discrete and Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Iterated medial triangle subdivision in surfaces of constant curvature tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 70 year: '2023' ... --- _id: '11991' abstract: - lang: eng text: The study of the complexity of the constraint satisfaction problem (CSP), centred around the Feder-Vardi Dichotomy Conjecture, has been very prominent in the last two decades. After a long concerted effort and many partial results, the Dichotomy Conjecture has been proved in 2017 independently by Bulatov and Zhuk. At about the same time, a vast generalisation of CSP, called promise CSP, has started to gain prominence. In this survey, we explain the importance of promise CSP and highlight many new very interesting features that the study of promise CSP has brought to light. The complexity classification quest for the promise CSP is wide open, and we argue that, despite the promise CSP being more general, this quest is rather more accessible to a wide range of researchers than the dichotomy-led study of the CSP has been. article_processing_charge: No article_type: original author: - first_name: Andrei full_name: Krokhin, Andrei last_name: Krokhin - first_name: Jakub full_name: Opršal, Jakub id: ec596741-c539-11ec-b829-c79322a91242 last_name: Opršal orcid: 0000-0003-1245-3456 citation: ama: Krokhin A, Opršal J. An invitation to the promise constraint satisfaction problem. ACM SIGLOG News. 2022;9(3):30-59. doi:10.1145/3559736.3559740 apa: Krokhin, A., & Opršal, J. (2022). An invitation to the promise constraint satisfaction problem. ACM SIGLOG News. Association for Computing Machinery. https://doi.org/10.1145/3559736.3559740 chicago: Krokhin, Andrei, and Jakub Opršal. “An Invitation to the Promise Constraint Satisfaction Problem.” ACM SIGLOG News. Association for Computing Machinery, 2022. https://doi.org/10.1145/3559736.3559740. ieee: A. Krokhin and J. Opršal, “An invitation to the promise constraint satisfaction problem,” ACM SIGLOG News, vol. 9, no. 3. Association for Computing Machinery, pp. 30–59, 2022. ista: Krokhin A, Opršal J. 2022. An invitation to the promise constraint satisfaction problem. ACM SIGLOG News. 9(3), 30–59. mla: Krokhin, Andrei, and Jakub Opršal. “An Invitation to the Promise Constraint Satisfaction Problem.” ACM SIGLOG News, vol. 9, no. 3, Association for Computing Machinery, 2022, pp. 30–59, doi:10.1145/3559736.3559740. short: A. Krokhin, J. Opršal, ACM SIGLOG News 9 (2022) 30–59. date_created: 2022-08-27T11:23:37Z date_published: 2022-07-01T00:00:00Z date_updated: 2022-09-05T08:19:38Z day: '01' department: - _id: UlWa doi: 10.1145/3559736.3559740 external_id: arxiv: - '2208.13538' intvolume: ' 9' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/2208.13538 month: '07' oa: 1 oa_version: Preprint page: 30-59 publication: ACM SIGLOG News publication_identifier: issn: - 2372-3491 publication_status: published publisher: Association for Computing Machinery quality_controlled: '1' status: public title: An invitation to the promise constraint satisfaction problem type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 9 year: '2022' ... --- _id: '11938' abstract: - lang: eng text: A matching is compatible to two or more labeled point sets of size n with labels {1, . . . , n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled sets of n points in convex position there exists a compatible matching with ⌊√2n + 1 − 1⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ). As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(log n) copies of any set of n points are necessary and sufficient for the existence of labelings of these point sets such that any compatible matching consists only of a single edge. acknowledgement: 'A.A. funded by the Marie Sklodowska-Curie grant agreement No 754411. Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23 (RiSE).' article_processing_charge: No article_type: original author: - first_name: Oswin full_name: Aichholzer, Oswin last_name: Aichholzer - first_name: Alan M full_name: Arroyo Guevara, Alan M id: 3207FDC6-F248-11E8-B48F-1D18A9856A87 last_name: Arroyo Guevara orcid: 0000-0003-2401-8670 - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 - first_name: Irene full_name: Parada, Irene last_name: Parada - first_name: Daniel full_name: Perz, Daniel last_name: Perz - first_name: Alexander full_name: Pilz, Alexander last_name: Pilz - first_name: Josef full_name: Tkadlec, Josef id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87 last_name: Tkadlec orcid: 0000-0002-1097-9684 - first_name: Birgit full_name: Vogtenhuber, Birgit last_name: Vogtenhuber citation: ama: Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. Journal of Graph Algorithms and Applications. 2022;26(2):225-240. doi:10.7155/jgaa.00591 apa: Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2022). On compatible matchings. Journal of Graph Algorithms and Applications. Brown University. https://doi.org/10.7155/jgaa.00591 chicago: Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” Journal of Graph Algorithms and Applications. Brown University, 2022. https://doi.org/10.7155/jgaa.00591. ieee: O. Aichholzer et al., “On compatible matchings,” Journal of Graph Algorithms and Applications, vol. 26, no. 2. Brown University, pp. 225–240, 2022. ista: Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec J, Vogtenhuber B. 2022. On compatible matchings. Journal of Graph Algorithms and Applications. 26(2), 225–240. mla: Aichholzer, Oswin, et al. “On Compatible Matchings.” Journal of Graph Algorithms and Applications, vol. 26, no. 2, Brown University, 2022, pp. 225–40, doi:10.7155/jgaa.00591. short: O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz, J. Tkadlec, B. Vogtenhuber, Journal of Graph Algorithms and Applications 26 (2022) 225–240. date_created: 2022-08-21T22:01:56Z date_published: 2022-06-01T00:00:00Z date_updated: 2023-02-23T13:54:21Z day: '01' ddc: - '000' department: - _id: UlWa - _id: HeEd - _id: KrCh doi: 10.7155/jgaa.00591 ec_funded: 1 external_id: arxiv: - '2101.03928' file: - access_level: open_access checksum: dc6e255e3558faff924fd9e370886c11 content_type: application/pdf creator: dernst date_created: 2022-08-22T06:42:42Z date_updated: 2022-08-22T06:42:42Z file_id: '11940' file_name: 2022_JourGraphAlgorithmsApplic_Aichholzer.pdf file_size: 694538 relation: main_file success: 1 file_date_updated: 2022-08-22T06:42:42Z has_accepted_license: '1' intvolume: ' 26' issue: '2' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 225-240 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: The Wittgenstein Prize - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 2584A770-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P 23499-N23 name: Modern Graph Algorithmic Techniques in Formal Verification - _id: 25863FF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11407 name: Game Theory publication: Journal of Graph Algorithms and Applications publication_identifier: issn: - 1526-1719 publication_status: published publisher: Brown University quality_controlled: '1' related_material: record: - id: '9296' relation: earlier_version status: public scopus_import: '1' status: public title: On compatible matchings tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 26 year: '2022' ... --- _id: '11777' abstract: - lang: eng text: "In this dissertation we study coboundary expansion of simplicial complex with a view of giving geometric applications.\r\nOur main novel tool is an equivariant version of Gromov's celebrated Topological Overlap Theorem. The equivariant topological overlap theorem leads to various geometric applications including a quantitative non-embeddability result for sufficiently thick buildings (which partially resolves a conjecture of Tancer and Vorwerk) and an improved lower bound on the pair-crossing number of (bounded degree) expander graphs. Additionally, we will give new proofs for several known lower bounds for geometric problems such as the number of Tverberg partitions or the crossing number of complete bipartite graphs.\r\nFor the aforementioned applications one is naturally lead to study expansion properties of joins of simplicial complexes. In the presence of a special certificate for expansion (as it is the case, e.g., for spherical buildings), the join of two expanders is an expander. On the flip-side, we report quite some evidence that coboundary expansion exhibits very non-product-like behaviour under taking joins. For instance, we exhibit infinite families of graphs $(G_n)_{n\\in \\mathbb{N}}$ and $(H_n)_{n\\in\\mathbb{N}}$ whose join $G_n*H_n$ has expansion of lower order than the product of the expansion constant of the graphs. Moreover, we show an upper bound of $(d+1)/2^d$ on the normalized coboundary expansion constants for the complete multipartite complex $[n]^{*(d+1)}$ (under a mild divisibility condition on $n$).\r\nVia the probabilistic method the latter result extends to an upper bound of $(d+1)/2^d+\\varepsilon$ on the coboundary expansion constant of the spherical building associated with $\\mathrm{PGL}_{d+2}(\\mathbb{F}_q)$ for any $\\varepsilon>0$ and sufficiently large $q=q(\\varepsilon)$. This disproves a conjecture of Lubotzky, Meshulam and Mozes -- in a rather strong sense.\r\nBy improving on existing lower bounds we make further progress towards closing the gap between the known lower and upper bounds on the coboundary expansion constants of $[n]^{*(d+1)}$. The best improvements we achieve using computer-aided proofs and flag algebras. The exact value even for the complete $3$-partite $2$-dimensional complex $[n]^{*3}$ remains unknown but we are happy to conjecture a precise value for every $n$. %Moreover, we show that a previously shown lower bound on the expansion constant of the spherical building associated with $\\mathrm{PGL}_{2}(\\mathbb{F}_q)$ is not tight.\r\nIn a loosely structured, last chapter of this thesis we collect further smaller observations related to expansion. We point out a link between discrete Morse theory and a technique for showing coboundary expansion, elaborate a bit on the hardness of computing coboundary expansion constants, propose a new criterion for coboundary expansion (in a very dense setting) and give one way of making the folklore result that expansion of links is a necessary condition for a simplicial complex to be an expander precise." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Pascal full_name: Wild, Pascal id: 4C20D868-F248-11E8-B48F-1D18A9856A87 last_name: Wild citation: ama: Wild P. High-dimensional expansion and crossing numbers of simplicial complexes. 2022. doi:10.15479/at:ista:11777 apa: Wild, P. (2022). High-dimensional expansion and crossing numbers of simplicial complexes. Institute of Science and Technology. https://doi.org/10.15479/at:ista:11777 chicago: Wild, Pascal. “High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes.” Institute of Science and Technology, 2022. https://doi.org/10.15479/at:ista:11777. ieee: P. Wild, “High-dimensional expansion and crossing numbers of simplicial complexes,” Institute of Science and Technology, 2022. ista: Wild P. 2022. High-dimensional expansion and crossing numbers of simplicial complexes. Institute of Science and Technology. mla: Wild, Pascal. High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes. Institute of Science and Technology, 2022, doi:10.15479/at:ista:11777. short: P. Wild, High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes, Institute of Science and Technology, 2022. date_created: 2022-08-10T15:51:19Z date_published: 2022-08-11T00:00:00Z date_updated: 2023-06-22T09:56:36Z day: '11' ddc: - '500' - '516' - '514' degree_awarded: PhD department: - _id: GradSch - _id: UlWa doi: 10.15479/at:ista:11777 ec_funded: 1 file: - access_level: open_access checksum: f5f3af1fb7c8a24b71ddc88ad7f7c5b4 content_type: text/x-python creator: pwild date_created: 2022-08-10T15:34:04Z date_updated: 2022-08-10T15:34:04Z description: Code for computer-assisted proofs in Section 8.4.7 in Thesis file_id: '11780' file_name: flags.py file_size: 16828 relation: supplementary_material - access_level: open_access checksum: 1f7c12dfe3bdaa9b147e4fbc3d34e3d5 content_type: text/x-c++src creator: pwild date_created: 2022-08-10T15:34:10Z date_updated: 2022-08-10T15:34:10Z description: Code for proof of Lemma 8.20 in Thesis file_id: '11781' file_name: lowerbound.cpp file_size: 12226 relation: supplementary_material - access_level: open_access checksum: 4cf81455c49e5dec3b9b2e3980137eeb content_type: text/x-python creator: pwild date_created: 2022-08-10T15:34:17Z date_updated: 2022-08-10T15:34:17Z description: Code for proof of Proposition 7.9 in Thesis file_id: '11782' file_name: upperbound.py file_size: 3240 relation: supplementary_material - access_level: open_access checksum: 4e96575b10cbe4e0d0db2045b2847774 content_type: application/pdf creator: pwild date_created: 2022-08-11T16:08:33Z date_updated: 2022-08-11T16:08:33Z file_id: '11809' file_name: finalthesisPascalWildPDFA.pdf file_size: 5086282 relation: main_file title: High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes - access_level: closed checksum: 92d94842a1fb6dca5808448137573b2e content_type: application/zip creator: pwild date_created: 2022-08-11T16:09:19Z date_updated: 2022-08-11T16:09:19Z file_id: '11810' file_name: ThesisSubmission.zip file_size: 18150068 relation: source_file file_date_updated: 2022-08-11T16:09:19Z has_accepted_license: '1' language: - iso: eng month: '08' oa: 1 oa_version: Published Version page: '170' project: - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program publication_identifier: isbn: - 978-3-99078-021-3 issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology status: public supervisor: - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 title: High-dimensional expansion and crossing numbers of simplicial complexes type: dissertation user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2022' ... --- _id: '10335' abstract: - lang: eng text: "Van der Holst and Pendavingh introduced a graph parameter σ, which coincides with the more famous Colin de Verdière graph parameter μ for small values. However, the definition of a is much more geometric/topological directly reflecting embeddability properties of the graph. They proved μ(G) ≤ σ(G) + 2 and conjectured σ(G) ≤ σ(G) for any graph G. We confirm this conjecture. As far as we know, this is the first topological upper bound on σ(G) which is, in general, tight.\r\nEquality between μ and σ does not hold in general as van der Holst and Pendavingh showed that there is a graph G with μ(G) ≤ 18 and σ(G) ≥ 20. We show that the gap appears at much smaller values, namely, we exhibit a graph H for which μ(H) ≥ 7 and σ(H) ≥ 8. We also prove that, in general, the gap can be large: The incidence graphs Hq of finite projective planes of order q satisfy μ(Hq) ∈ O(q3/2) and σ(Hq) ≥ q2." acknowledgement: 'V. K. gratefully acknowledges the support of Austrian Science Fund (FWF): P 30902-N35. This work was done mostly while he was employed at the University of Innsbruck. During the early stage of this research, V. K. was partially supported by Charles University project GAUK 926416. M. T. is supported by the grant no. 19-04113Y of the Czech Science Foundation(GA ˇCR) and partially supported by Charles University project UNCE/SCI/004.' article_processing_charge: No article_type: original author: - first_name: Vojtech full_name: Kaluza, Vojtech id: 21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E last_name: Kaluza orcid: 0000-0002-2512-8698 - first_name: Martin full_name: Tancer, Martin id: 38AC689C-F248-11E8-B48F-1D18A9856A87 last_name: Tancer orcid: 0000-0002-1191-6714 citation: ama: Kaluza V, Tancer M. Even maps, the Colin de Verdière number and representations of graphs. Combinatorica. 2022;42:1317-1345. doi:10.1007/s00493-021-4443-7 apa: Kaluza, V., & Tancer, M. (2022). Even maps, the Colin de Verdière number and representations of graphs. Combinatorica. Springer Nature. https://doi.org/10.1007/s00493-021-4443-7 chicago: Kaluza, Vojtech, and Martin Tancer. “Even Maps, the Colin de Verdière Number and Representations of Graphs.” Combinatorica. Springer Nature, 2022. https://doi.org/10.1007/s00493-021-4443-7. ieee: V. Kaluza and M. Tancer, “Even maps, the Colin de Verdière number and representations of graphs,” Combinatorica, vol. 42. Springer Nature, pp. 1317–1345, 2022. ista: Kaluza V, Tancer M. 2022. Even maps, the Colin de Verdière number and representations of graphs. Combinatorica. 42, 1317–1345. mla: Kaluza, Vojtech, and Martin Tancer. “Even Maps, the Colin de Verdière Number and Representations of Graphs.” Combinatorica, vol. 42, Springer Nature, 2022, pp. 1317–45, doi:10.1007/s00493-021-4443-7. short: V. Kaluza, M. Tancer, Combinatorica 42 (2022) 1317–1345. date_created: 2021-11-25T13:49:16Z date_published: 2022-12-01T00:00:00Z date_updated: 2023-08-02T06:43:27Z day: '01' ddc: - '514' - '516' department: - _id: UlWa doi: 10.1007/s00493-021-4443-7 external_id: arxiv: - '1907.05055' isi: - '000798210100003' intvolume: ' 42' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.1907.05055' month: '12' oa: 1 oa_version: Preprint page: 1317-1345 publication: Combinatorica publication_identifier: issn: - 0209-9683 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Even maps, the Colin de Verdière number and representations of graphs type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 42 year: '2022' ... --- _id: '10776' abstract: - lang: eng text: 'Let K be a convex body in Rn (i.e., a compact convex set with nonempty interior). Given a point p in the interior of K, a hyperplane h passing through p is called barycentric if p is the barycenter of K∩h. In 1961, Grünbaum raised the question whether, for every K, there exists an interior point p through which there are at least n+1 distinct barycentric hyperplanes. Two years later, this was seemingly resolved affirmatively by showing that this is the case if p=p0 is the point of maximal depth in K. However, while working on a related question, we noticed that one of the auxiliary claims in the proof is incorrect. Here, we provide a counterexample; this re-opens Grünbaum’s question. It follows from known results that for n≥2, there are always at least three distinct barycentric cuts through the point p0∈K of maximal depth. Using tools related to Morse theory we are able to improve this bound: four distinct barycentric cuts through p0 are guaranteed if n≥3.' acknowledgement: The work by Zuzana Patáková has been partially supported by Charles University Research Center Program No. UNCE/SCI/022, and part of it was done during her research stay at IST Austria. The work by Martin Tancer is supported by the GAČR Grant 19-04113Y and by the Charles University Projects PRIMUS/17/SCI/3 and UNCE/SCI/004. article_processing_charge: No article_type: original author: - first_name: Zuzana full_name: Patakova, Zuzana id: 48B57058-F248-11E8-B48F-1D18A9856A87 last_name: Patakova orcid: 0000-0002-3975-1683 - first_name: Martin full_name: Tancer, Martin last_name: Tancer - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: Patakova Z, Tancer M, Wagner U. Barycentric cuts through a convex body. Discrete and Computational Geometry. 2022;68:1133-1154. doi:10.1007/s00454-021-00364-7 apa: Patakova, Z., Tancer, M., & Wagner, U. (2022). Barycentric cuts through a convex body. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-021-00364-7 chicago: Patakova, Zuzana, Martin Tancer, and Uli Wagner. “Barycentric Cuts through a Convex Body.” Discrete and Computational Geometry. Springer Nature, 2022. https://doi.org/10.1007/s00454-021-00364-7. ieee: Z. Patakova, M. Tancer, and U. Wagner, “Barycentric cuts through a convex body,” Discrete and Computational Geometry, vol. 68. Springer Nature, pp. 1133–1154, 2022. ista: Patakova Z, Tancer M, Wagner U. 2022. Barycentric cuts through a convex body. Discrete and Computational Geometry. 68, 1133–1154. mla: Patakova, Zuzana, et al. “Barycentric Cuts through a Convex Body.” Discrete and Computational Geometry, vol. 68, Springer Nature, 2022, pp. 1133–54, doi:10.1007/s00454-021-00364-7. short: Z. Patakova, M. Tancer, U. Wagner, Discrete and Computational Geometry 68 (2022) 1133–1154. date_created: 2022-02-20T23:01:35Z date_published: 2022-12-01T00:00:00Z date_updated: 2023-08-02T14:38:58Z day: '01' department: - _id: UlWa doi: 10.1007/s00454-021-00364-7 external_id: arxiv: - '2003.13536' isi: - '000750681500001' intvolume: ' 68' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2003.13536 month: '12' oa: 1 oa_version: Preprint page: 1133-1154 publication: Discrete and Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Barycentric cuts through a convex body type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 68 year: '2022' ... --- _id: '10887' abstract: - lang: eng text: "We introduce a new way of representing logarithmically concave functions on Rd. It allows us to extend the notion of the largest volume ellipsoid contained in a convex body to the setting of logarithmically concave functions as follows. For every s>0, we define a class of non-negative functions on Rd derived from ellipsoids in Rd+1. For any log-concave function f on Rd , and any fixed s>0, we consider functions belonging to this class, and find the one with the largest integral under the condition that it is pointwise less than or equal to f, and we call it the John s-function of f. After establishing existence and uniqueness, we give a characterization of this function similar to the one given by John in his fundamental theorem. We find that John s-functions converge to characteristic functions of ellipsoids as s tends to zero and to Gaussian densities as s tends to infinity.\r\nAs an application, we prove a quantitative Helly type result: the integral of the pointwise minimum of any family of log-concave functions is at least a constant cd multiple of the integral of the pointwise minimum of a properly chosen subfamily of size 3d+2, where cd depends only on d." acknowledgement: 'G.I. was supported by the Ministry of Education and Science of the Russian Federation in the framework of MegaGrant no 075-15-2019-1926. M.N. was supported by the National Research, Development and Innovation Fund (NRDI) grants K119670 and KKP-133864 as well as the Bolyai Scholarship of the Hungarian Academy of Sciences and the New National Excellence Programme and the TKP2020-NKA-06 program provided by the NRDI. ' article_number: '109441' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Grigory full_name: Ivanov, Grigory id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E last_name: Ivanov - first_name: Márton full_name: Naszódi, Márton last_name: Naszódi citation: ama: Ivanov G, Naszódi M. Functional John ellipsoids. Journal of Functional Analysis. 2022;282(11). doi:10.1016/j.jfa.2022.109441 apa: Ivanov, G., & Naszódi, M. (2022). Functional John ellipsoids. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2022.109441 chicago: Ivanov, Grigory, and Márton Naszódi. “Functional John Ellipsoids.” Journal of Functional Analysis. Elsevier, 2022. https://doi.org/10.1016/j.jfa.2022.109441. ieee: G. Ivanov and M. Naszódi, “Functional John ellipsoids,” Journal of Functional Analysis, vol. 282, no. 11. Elsevier, 2022. ista: Ivanov G, Naszódi M. 2022. Functional John ellipsoids. Journal of Functional Analysis. 282(11), 109441. mla: Ivanov, Grigory, and Márton Naszódi. “Functional John Ellipsoids.” Journal of Functional Analysis, vol. 282, no. 11, 109441, Elsevier, 2022, doi:10.1016/j.jfa.2022.109441. short: G. Ivanov, M. Naszódi, Journal of Functional Analysis 282 (2022). date_created: 2022-03-20T23:01:38Z date_published: 2022-06-01T00:00:00Z date_updated: 2023-08-02T14:51:11Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.1016/j.jfa.2022.109441 external_id: arxiv: - '2006.09934' isi: - '000781371300008' file: - access_level: open_access checksum: 1cf185e264e04c87cb1ce67a00db88ab content_type: application/pdf creator: dernst date_created: 2022-08-02T10:40:48Z date_updated: 2022-08-02T10:40:48Z file_id: '11721' file_name: 2022_JourFunctionalAnalysis_Ivanov.pdf file_size: 734482 relation: main_file success: 1 file_date_updated: 2022-08-02T10:40:48Z has_accepted_license: '1' intvolume: ' 282' isi: 1 issue: '11' language: - iso: eng month: '06' oa: 1 oa_version: Published Version publication: Journal of Functional Analysis publication_identifier: eissn: - 1096-0783 issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Functional John ellipsoids tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 282 year: '2022' ...