---
_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'
...