| Autor: |
Naszódi, Márton, Swanepoel, Konrad J. |
| Rok vydání: |
2017 |
| Předmět: |
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| Zdroj: |
Contributions to Discrete Mathematics 13 (2018), 116--123 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.11575/cdm.v13i2.62732 |
| Popis: |
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 $2\cdot 3^d$ members. This improves a result of Polyanskii (arXiv:1610.04400). Using similar ideas, we also give a proof the following result of Polyanskii: Let $K_1,\dots,K_n$ be a sequence of homothets of the o-symmetric convex body $K$, such that for any $iComment: 9 pages |
| Databáze: |
arXiv |
| Externí odkaz: |
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