Cardinalities of k-distance sets in Minkowski spaces

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dc.creatorSwanepoel, Konrad J.
dc.date2007-12-06
dc.date.accessioned2026-07-07T08:47:40Z
dc.date.available2026-07-07T08:47:40Z
dc.descriptionA 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.
dc.description7 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/0712.0953
dc.identifierhttp://arxiv.org/abs/0712.0953
dc.identifierDiscrete Mathematics 197/198 (1999) 759-767
dc.identifierdoi:10.1090/S0002-9939-96-03370-9
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/143681
dc.subjectMetric Geometry
dc.subjectCombinatorics
dc.subject52C10
dc.titleCardinalities of k-distance sets in Minkowski spaces
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