  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 $i<j$, the center of $K_j$ lies on the boundary of
$K_i$. Then $n\leq O(3^d d)$.

Metric Geometry;Combinatorics