Unit distances and diameters in Euclidean spaces

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dc.creatorSwanepoel, Konrad J
dc.date2007-07-02
dc.date.accessioned2026-07-07T12:51:00Z
dc.date.available2026-07-07T12:51:00Z
dc.descriptionWe show that the maximum number of unit distances or of diameters in a set of n points in d-dimensional Euclidean space is attained only by specific types of Lenz constructions, for all d >= 4 and n sufficiently large, depending on d. As a corollary we determine the exact maximum number of unit distances for all even d >= 6, and the exact maximum number of diameters for all d >= 4, for all $n$ sufficiently large, depending on d.
dc.identifierhttps://arxiv.org/abs/0707.0213
dc.identifierhttp://arxiv.org/abs/0707.0213
dc.identifierDiscrete and Computational Geometry 49 (2009), 1--27.
dc.identifierdoi:10.1007/s00454-008-9082-x
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222859
dc.subjectMetric Geometry
dc.subjectCombinatorics
dc.subject52C10
dc.titleUnit distances and diameters in Euclidean spaces
dc.typetext

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