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Arrangements of homothets of a convex body

Naszódi, Márton, Pach, János and Swanepoel, Konrad ORCID: 0000-0002-1668-887X (2017) Arrangements of homothets of a convex body. Mathematika, 63 (2). 696 - 710. ISSN 0025-5793

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Identification Number: 10.1112/S0025579317000122


Answering a question of F\"uredi and Loeb (1994), we show that the maximum number of pairwise intersecting homothets of a d-dimensional centrally symmetric convex body K, none of which contains the center of another in its interior, is at most O(3ddlogd). If K is not necessarily centrally symmetric and the role of its center is played by its centroid, then the above bound can be replaced by O(3d(2dd)dlogd). We establish analogous results for the case where the center is defined as an arbitrary point in the interior of K. We also show that in the latter case, one can always find families of at least Ω((2/3–√)d) translates of K with the above property.

Item Type: Article
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Additional Information: © 2017 University College London
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 07 Jun 2017 10:49
Last Modified: 16 May 2024 02:32

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