[{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1808.09165"}],"oa":1,"publication_identifier":{"issn":["0012365X"]},"type":"journal_article","date_published":"2021-05-01T00:00:00Z","language":[{"iso":"eng"}],"article_number":"112312","month":"05","oa_version":"Preprint","publication":"Discrete Mathematics","volume":344,"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).","abstract":[{"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.","lang":"eng"}],"day":"01","arxiv":1,"doi":"10.1016/j.disc.2021.112312","external_id":{"arxiv":["1808.09165"],"isi":["000633365200001"]},"isi":1,"year":"2021","citation":{"ista":"Ivanov G. 2021. On the volume of projections of the cross-polytope. Discrete Mathematics. 344(5), 112312.","short":"G. Ivanov, Discrete Mathematics 344 (2021).","mla":"Ivanov, Grigory. “On the Volume of Projections of the Cross-Polytope.” <i>Discrete Mathematics</i>, vol. 344, no. 5, 112312, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.disc.2021.112312\">10.1016/j.disc.2021.112312</a>.","chicago":"Ivanov, Grigory. “On the Volume of Projections of the Cross-Polytope.” <i>Discrete Mathematics</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.disc.2021.112312\">https://doi.org/10.1016/j.disc.2021.112312</a>.","ieee":"G. Ivanov, “On the volume of projections of the cross-polytope,” <i>Discrete Mathematics</i>, vol. 344, no. 5. Elsevier, 2021.","apa":"Ivanov, G. (2021). On the volume of projections of the cross-polytope. <i>Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.disc.2021.112312\">https://doi.org/10.1016/j.disc.2021.112312</a>","ama":"Ivanov G. On the volume of projections of the cross-polytope. <i>Discrete Mathematics</i>. 2021;344(5). doi:<a href=\"https://doi.org/10.1016/j.disc.2021.112312\">10.1016/j.disc.2021.112312</a>"},"date_updated":"2023-08-07T13:40:37Z","article_type":"original","publisher":"Elsevier","quality_controlled":"1","intvolume":"       344","title":"On the volume of projections of the cross-polytope","article_processing_charge":"No","department":[{"_id":"UlWa"}],"date_created":"2021-02-07T23:01:12Z","publication_status":"published","issue":"5","author":[{"id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","full_name":"Ivanov, Grigory","first_name":"Grigory","last_name":"Ivanov"}],"scopus_import":"1","_id":"9098"}]