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Arrangements of Homothets of a Convex Body II

Marton Naszodi, Konrad Swanepoel
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 Polyanskii: Let K_1,....,K_n be a
more » ... K_1,....,K_n be a sequence of homothets of the o-symmetric convex body K, such that for any i
doi:10.11575/cdm.v13i2.62732 fatcat:3m2lnactwncjdelmbhdepau2ie