Pairwise intersecting homothets of a convex body

Abstract

We show that the maximum number of pairwise intersecting positive homothets of a $d$-dimensional centrally symmetric convex body, none of which contains the center of another in its interior, is at most $3^{d+1}$. Also, we improve upper bounds for cardinalities of $k$-distance sets in Minkowski spaces.

v2: 8 pages, 2 figures, corrections are made in the proof of Lemma 3, Discrete Mathematics, accepted

References in corpus (1)

• Combinatorial distance geometry in normed spaces

Cited by in corpus (4)

• Combinatorial distance geometry in normed spaces
• Arrangements of homothets of a convex body
• Odd-distance and right-equidistant sets in the maximum and Manhattan metrics
• Monochromatic infinite sets in Minkowski planes