Cardinalities of k-distance sets in Minkowski spaces (1999)
by
K. J. Swanepoel
| Venue: | Discrete Mathematics |
| Citations: | 2 - 0 self |
BibTeX
@ARTICLE{Swanepoel99cardinalitiesof,
author = {K. J. Swanepoel},
title = {Cardinalities of k-distance sets in Minkowski spaces},
journal = {Discrete Mathematics},
year = {1999},
pages = {759767}
}
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Abstract
Abstract. A subset of a metric space is a k-distance set if there are exactly k non-zero distances occuring 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 2-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. 1.
