Cookies?
Library Header Image
LSE Research Online LSE Library Services

Cardinalities of k-distance sets in Minkowski spaces

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

Full text not available from this repository.
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
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 09 Oct 2009 09:37
Last Modified: 01 Oct 2010 09:27
URI: http://eprints.lse.ac.uk/id/eprint/25415

Actions (login required)

View Item View Item