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

## 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 |
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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 |

Date Deposited: | 09 Oct 2009 09:37 |

URL: | http://eprints.lse.ac.uk/25415/ |

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