Name
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). |
Year | DOI | Venue |
|---|---|---|
2018 | 10.11575/cdm.v13i2.62732 | CONTRIBUTIONS TO DISCRETE MATHEMATICS |
Keywords | Field | DocType |
homothets,convex bodies,Minkowski arrangements,packing | Combinatorics,Convex body,Euclidean space,Minkowski space,Mathematics | Journal |
Volume | Issue | ISSN |
13 | 2 | 1715-0868 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Marton Naszodi | 1 | 21 | 7.87 |
| Konrad J. Swanepoel | 2 | 57 | 14.22 |