[{"department":[{"tree":[{"_id":"ResearchGroups"},{"_id":"IST"}],"_id":"UlWa"}],"date_updated":"2023-08-07T13:40:37Z","creator":{"id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","login":"dernst"},"type":"journal_article","article_type":"original","status":"public","_id":"9098","issue":"5","volume":344,"publication_status":"published","publication_identifier":{"issn":[]},"language":[{}],"main_file_link":[{"url":"https://arxiv.org/abs/1808.09165","open_access":"1"}],"scopus_import":"1","intvolume":" 344","month":"05","abstract":[{"lang":"eng"}],"oa_version":"Preprint","external_id":{"arxiv":[],"isi":[]},"article_processing_charge":"No","author":[{"first_name":"Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","last_name":"Ivanov"}],"citation":{"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.","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.","ieee":"G. Ivanov, “On the volume of projections of the cross-polytope,” Discrete Mathematics, vol. 344, no. 5. Elsevier, 2021.","short":"G. Ivanov, Discrete Mathematics 344 (2021).","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"},"dini_type":"doc-type:article","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_number":"112312","uri_base":"https://research-explorer.ista.ac.at","date_created":"2021-02-07T23:01:12Z","date_published":"2021-05-01T00:00:00Z","isi":1,"dc":{"date":["2021"],"publisher":["Elsevier"],"type":["info:eu-repo/semantics/article","doc-type:article","text","http://purl.org/coar/resource_type/c_6501"],"source":["Ivanov G. On the volume of projections of the cross-polytope. Discrete Mathematics. 2021;344(5). doi:10.1016/j.disc.2021.112312"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1016/j.disc.2021.112312","info:eu-repo/semantics/altIdentifier/issn/0012365X","info:eu-repo/semantics/altIdentifier/wos/000633365200001","info:eu-repo/semantics/altIdentifier/arxiv/1808.09165"],"description":["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."],"identifier":["https://research-explorer.ista.ac.at/record/9098"],"title":["On the volume of projections of the cross-polytope"],"creator":["Ivanov, Grigory"],"rights":["info:eu-repo/semantics/openAccess"],"language":["eng"]},"publication":"Discrete Mathematics","day":"01","oa":1,"quality_controlled":"1","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)."}]