Arrangements of homothets of a convex body II

Naszódi, Márton and Swanepoel, Konrad ORCID: 0000-0002-1668-887X (2018) Arrangements of homothets of a convex body II. Contributions to Discrete Mathematics, 13 (2). 116 - 123. ISSN 1715-0868

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Abstract

A family of homothets of an o-symmetric convex body K in d-dimensional Euclidean space is called a Minkowski arrangement if no homothet contains the center of any other homothet in its interior. We show that any pairwise intersecting Minkowski arrangement of a ddimensional convex body has at most 2 · 3d members. This improves a result of Polyanskii (Discrete Mathematics 340 (2017), 1950–1956). Using similar ideas, we also give a proof the following result of Polyanskii: Let K1, . . . , Kn be a sequence of homothets of the o-symmetric convex body K, such that for any i < j, the center of Kj lies on the boundary of Ki. Then n = O(3dd).

Item Type:	Article
Official URL:	https://cdm.ucalgary.ca/index
Additional Information:	© 2018 University of Calgary
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	19 Mar 2018 15:44
Last Modified:	12 Dec 2024 01:37
Projects:	K119670
Funders:	National Research, Development and Innovation Fund; UNKP-17-4 New National Excellence Program of the Ministry of Human Capacities
URI:	http://eprints.lse.ac.uk/id/eprint/87297

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