Pairwise intersecting homothets of a convex body
Alexandr Polyanskii

TL;DR
This paper establishes an upper bound on the number of pairwise intersecting homothets of a convex body in high-dimensional space and improves bounds for k-distance sets in Minkowski spaces.
Contribution
It provides a new upper bound for the maximum number of pairwise intersecting homothets of a convex body and enhances bounds for k-distance sets in Minkowski spaces.
Findings
Maximum of 3^{d+1} pairwise intersecting homothets in d-dimensional space.
Improved upper bounds for k-distance sets in Minkowski spaces.
Applicable to centrally symmetric convex bodies.
Abstract
We show that the maximum number of pairwise intersecting positive homothets of a -dimensional centrally symmetric convex body, none of which contains the center of another in its interior, is at most . Also, we improve upper bounds for cardinalities of -distance sets in Minkowski spaces.
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