Naszódi, Márton and Swanepoel Konrad J., (2018) ARRANGEMENTS OF HOMOTHETS OF A CONVEX BODY II. CONTRIBUTIONS TO DISCRETE MATHEMATICS, 13 (2). pp. 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 d-dimensional convex body has at most 2 . 3(d) 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 Polyan- skii: Let , K-1, ... ,K-n be a sequence of homothets of the o-symmetric convex body K, such that for any i < j, the center of K-j lies on the boundary of K-i. Then n = O(3(d)d).
| Item Type: | Article |
|---|---|
| Additional Information: | Funding Agency and Grant Number: National Research, Development and Innovation Fund [K119670]; Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences; Ministry of Human Capacities [UNKP-17-4] Funding text: M. N. was partially supported by the National Research, Development and Innovation Fund grant K119670, the Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences and the UNKP-17-4 New National Excellence Program of the Ministry of Human Capacities. |
| Uncontrolled Keywords: | Homothets; Convex bodies; Minkowski arrangements; |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 22 Sep 2019 14:34 |
| Last Modified: | 22 Sep 2019 14:34 |
| URI: | http://real.mtak.hu/id/eprint/100306 |
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