--- _id: '9098' abstract: - lang: eng text: "We study properties of the volume of projections of the n-dimensional\r\ncross-polytope $\\crosp^n = \\{ x \\in \\R^n \\mid |x_1| + \\dots + |x_n| \\leqslant 1\\}.$ We prove that the projection of $\\crosp^n$ onto a k-dimensional coordinate subspace has the maximum possible volume for k=2 and for k=3.\r\nWe obtain the exact lower bound on the volume of such a projection onto a two-dimensional plane. Also, we show that there exist local maxima which are not global ones for the volume of a projection of $\\crosp^n$ onto a k-dimensional subspace for any n>k⩾2." acknowledgement: Research was supported by the Russian Foundation for Basic Research, project 18-01-00036A (Theorems 1.5 and 5.3) and by the Ministry of Education and Science of the Russian Federation in the framework of MegaGrant no 075-15-2019-1926 (Theorems 1.2 and 7.3). article_number: '112312' article_processing_charge: No article_type: original author: - first_name: Grigory full_name: Ivanov, Grigory id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E last_name: Ivanov citation: ama: Ivanov G. On the volume of projections of the cross-polytope. Discrete Mathematics. 2021;344(5). doi:10.1016/j.disc.2021.112312 apa: Ivanov, G. (2021). On the volume of projections of the cross-polytope. Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.disc.2021.112312 chicago: Ivanov, Grigory. “On the Volume of Projections of the Cross-Polytope.” Discrete Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.disc.2021.112312. ieee: G. Ivanov, “On the volume of projections of the cross-polytope,” Discrete Mathematics, vol. 344, no. 5. Elsevier, 2021. ista: Ivanov G. 2021. On the volume of projections of the cross-polytope. Discrete Mathematics. 344(5), 112312. mla: Ivanov, Grigory. “On the Volume of Projections of the Cross-Polytope.” Discrete Mathematics, vol. 344, no. 5, 112312, Elsevier, 2021, doi:10.1016/j.disc.2021.112312. short: G. Ivanov, Discrete Mathematics 344 (2021). date_created: 2021-02-07T23:01:12Z date_published: 2021-05-01T00:00:00Z date_updated: 2023-08-07T13:40:37Z day: '01' department: - _id: UlWa doi: 10.1016/j.disc.2021.112312 external_id: arxiv: - '1808.09165' isi: - '000633365200001' intvolume: ' 344' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1808.09165 month: '05' oa: 1 oa_version: Preprint publication: Discrete Mathematics publication_identifier: issn: - 0012365X publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: On the volume of projections of the cross-polytope type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 344 year: '2021' ...