Swanepoel, Konrad (1999) Cardinalities of k-distance sets in Minkowski spaces. Discrete mathematics, 197/19 . pp. 759-767. ISSN 0012-365X
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.
|Additional Information:||© 1999 Elsevier|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
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