Cardinalities of k-distance sets in Minkowski spaces

Swanepoel, Konrad ORCID: 0000-0002-1668-887X (1999) Cardinalities of k-distance sets in Minkowski spaces. Discrete Mathematics, 197/19. pp. 759-767. ISSN 0012-365X

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Identification Number: 10.1016/S0012-365X(99)90143-7

Abstract

A subset of a metric space is a k-distance set if there are exactly k non-zero distances occurring between points. We conjecture that a k-distance set in a d-dimensional Banach space (or Minkowski space), contains at most (k − 1)d points, with equality iff the unit ball is a parallelotope. We solve this conjecture in the affirmative for all two-dimensional spaces and for spaces where the unit ball is a parallelotope. For general spaces we find various weaker upper bounds for k-distance sets.

Item Type:	Article
Official URL:	http://www.elsevier.com/wps/find/journaldescriptio...
Additional Information:	© 1999 Elsevier
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	09 Oct 2009 09:37
Last Modified:	11 Dec 2024 22:10
URI:	http://eprints.lse.ac.uk/id/eprint/25415

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