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