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Arrangements of homothets of a convex body II

Naszódi, Márton and Swanepoel, Konrad (2017) Arrangements of homothets of a convex body II. Discrete Mathematics, 63 (2). pp. 696-710. ISSN 0012-365X

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Identification Number: 10.1112/S0025579317000122

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://www.journals.elsevier.com/discrete-mathema...
Additional Information: © 2018 Elsevier
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 19 Mar 2018 15:44
Last Modified: 20 Feb 2019 12:24
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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