[{"extern":"1","publist_id":"7993","abstract":[{"lang":"eng","text":"We prove that there is no strongly regular graph (SRG) with parameters (460; 153; 32; 60). The proof is based on a recent lower bound on the number of 4-cliques in a SRG and some applications of Euclidean representation of SRGs. "}],"type":"book_chapter","oa_version":"Preprint","date_updated":"2021-01-12T08:06:06Z","date_created":"2018-12-11T11:44:25Z","author":[{"last_name":"Bondarenko","first_name":"Andriy","full_name":"Bondarenko, Andriy"},{"id":"388D3134-F248-11E8-B48F-1D18A9856A87","last_name":"Mellit","first_name":"Anton","full_name":"Mellit, Anton"},{"full_name":"Prymak, Andriy","last_name":"Prymak","first_name":"Andriy"},{"full_name":"Radchenko, Danylo","first_name":"Danylo","last_name":"Radchenko"},{"full_name":"Viazovska, Maryna","last_name":"Viazovska","first_name":"Maryna"}],"department":[{"_id":"TaHa"}],"publisher":"Springer","title":"There is no strongly regular graph with parameters (460; 153; 32; 60)","publication_status":"published","status":"public","_id":"61","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","year":"2018","article_processing_charge":"No","month":"05","day":"23","language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-72456-0_7","date_published":"2018-05-23T00:00:00Z","page":"131 - 134","quality_controlled":"1","external_id":{"arxiv":["1509.06286"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1509.06286"}],"citation":{"short":"A. Bondarenko, A. Mellit, A. Prymak, D. Radchenko, M. Viazovska, in:, Contemporary Computational Mathematics, Springer, 2018, pp. 131–134.","mla":"Bondarenko, Andriy, et al. “There Is No Strongly Regular Graph with Parameters (460; 153; 32; 60).” Contemporary Computational Mathematics, Springer, 2018, pp. 131–34, doi:10.1007/978-3-319-72456-0_7.","chicago":"Bondarenko, Andriy, Anton Mellit, Andriy Prymak, Danylo Radchenko, and Maryna Viazovska. “There Is No Strongly Regular Graph with Parameters (460; 153; 32; 60).” In Contemporary Computational Mathematics, 131–34. Springer, 2018. https://doi.org/10.1007/978-3-319-72456-0_7.","ama":"Bondarenko A, Mellit A, Prymak A, Radchenko D, Viazovska M. There is no strongly regular graph with parameters (460; 153; 32; 60). In: Contemporary Computational Mathematics. Springer; 2018:131-134. doi:10.1007/978-3-319-72456-0_7","ieee":"A. Bondarenko, A. Mellit, A. Prymak, D. Radchenko, and M. Viazovska, “There is no strongly regular graph with parameters (460; 153; 32; 60),” in Contemporary Computational Mathematics, Springer, 2018, pp. 131–134.","apa":"Bondarenko, A., Mellit, A., Prymak, A., Radchenko, D., & Viazovska, M. (2018). There is no strongly regular graph with parameters (460; 153; 32; 60). In Contemporary Computational Mathematics (pp. 131–134). Springer. https://doi.org/10.1007/978-3-319-72456-0_7","ista":"Bondarenko A, Mellit A, Prymak A, Radchenko D, Viazovska M. 2018.There is no strongly regular graph with parameters (460; 153; 32; 60). In: Contemporary Computational Mathematics. , 131–134."},"publication":"Contemporary Computational Mathematics"},{"scopus_import":1,"month":"01","day":"01","publication_identifier":{"isbn":["9780198802013","9780191840500"]},"publication":"Geometry and Physics: Volume I","citation":{"short":"T. Hausel, A. Mellit, D. Pei, in:, Geometry and Physics: Volume I, Oxford University Press, 2018, pp. 189–218.","mla":"Hausel, Tamás, et al. “Mirror Symmetry with Branes by Equivariant Verlinde Formulas.” Geometry and Physics: Volume I, Oxford University Press, 2018, pp. 189–218, doi:10.1093/oso/9780198802013.003.0009.","chicago":"Hausel, Tamás, Anton Mellit, and Du Pei. “Mirror Symmetry with Branes by Equivariant Verlinde Formulas.” In Geometry and Physics: Volume I, 189–218. Oxford University Press, 2018. https://doi.org/10.1093/oso/9780198802013.003.0009.","ama":"Hausel T, Mellit A, Pei D. Mirror symmetry with branes by equivariant verlinde formulas. In: Geometry and Physics: Volume I. Oxford University Press; 2018:189-218. doi:10.1093/oso/9780198802013.003.0009","apa":"Hausel, T., Mellit, A., & Pei, D. (2018). Mirror symmetry with branes by equivariant verlinde formulas. In Geometry and Physics: Volume I (pp. 189–218). Oxford University Press. https://doi.org/10.1093/oso/9780198802013.003.0009","ieee":"T. Hausel, A. Mellit, and D. Pei, “Mirror symmetry with branes by equivariant verlinde formulas,” in Geometry and Physics: Volume I, Oxford University Press, 2018, pp. 189–218.","ista":"Hausel T, Mellit A, Pei D. 2018.Mirror symmetry with branes by equivariant verlinde formulas. In: Geometry and Physics: Volume I. , 189–218."},"quality_controlled":"1","page":"189-218","doi":"10.1093/oso/9780198802013.003.0009","date_published":"2018-01-01T00:00:00Z","language":[{"iso":"eng"}],"type":"book_chapter","abstract":[{"text":"This chapter finds an agreement of equivariant indices of semi-classical homomorphisms between pairwise mirror branes in the GL2 Higgs moduli space on a Riemann surface. On one side of the agreement, components of the Lagrangian brane of U(1,1) Higgs bundles, whose mirror was proposed by Hitchin to be certain even exterior powers of the hyperholomorphic Dirac bundle on the SL2 Higgs moduli space, are present. The agreement arises from a mysterious functional equation. This gives strong computational evidence for Hitchin’s proposal.","lang":"eng"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"6525","year":"2018","title":"Mirror symmetry with branes by equivariant verlinde formulas","publication_status":"published","status":"public","department":[{"_id":"TaHa"}],"publisher":"Oxford University Press","author":[{"full_name":"Hausel, Tamás","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","last_name":"Hausel","first_name":"Tamás"},{"full_name":"Mellit, Anton","id":"388D3134-F248-11E8-B48F-1D18A9856A87","last_name":"Mellit","first_name":"Anton"},{"last_name":"Pei","first_name":"Du","full_name":"Pei, Du"}],"date_created":"2019-06-06T12:42:01Z","date_updated":"2021-01-12T08:07:52Z","oa_version":"None"}]