Pairwise intersecting homothets of a convex body

DOI10.1016/j.endm.2017.07.065zbMath1383.52004arXiv1610.04400OpenAlexW2755911414MaRDI QIDQ5915835

Aleksandr A. Polyanskii

Publication date: 18 January 2018

Published in: Electronic Notes in Discrete Mathematics, Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.04400

zbMATH Keywords

cardinalitycentrally symmetric convex body\(k\)-distance set\(k\)-distance setsMinkowski arrangementpairwise intersecting homothets\(0\)-symmetric convex body

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items

On generalized Minkowski arrangements, Bounds on convex bodies in pairwise intersecting Minkowski arrangement of order \(\mu\), Odd-distance sets and right-equidistant sequences in the maximum and Manhattan metrics, ARRANGEMENTS OF HOMOTHETS OF A CONVEX BODY, Intersecting diametral balls induced by a geometric graph, Arrangements of homothets of a convex body II, Pairwise intersecting homothets of a convex body, Odd-distance and right-equidistant sets in the maximum and Manhattan metrics

Cites Work

• Cardinalities of \(k\)-distance sets in Minkowski spaces
• On a conjecture of Károly Bezdek and János Pach
• Über zwei Probleme bezüglich konvexer Körper von P. Erdős und von V.L. Klee
• On the Bezdek–Pach Conjecture for Centrally Symmetric Convex Bodies
• On the Best Constant for the Besicovitch Covering Theorem
• ARRANGEMENTS OF HOMOTHETS OF A CONVEX BODY
• Minkowskian Distribution of Discs
• Equilateral Sets in Minkowski Spaces
• Pairwise intersecting homothets of a convex body