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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

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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
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 09 Oct 2009 09:37
URL: http://eprints.lse.ac.uk/25415/

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