A problem of Kusner on equilateral sets期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A problem of Kusner on equilateral sets

Authors:	K.?J.?Swanepoel author-information" > author-information__contact u-icon-before" > mailto:swanekj@unisa.ac.za" title=" swanekj@unisa.ac.za" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author

Affiliation:	(1) Department of Mathematics, Applied Mathematics and Astronomy, University of South Africa, P.O. Box 392, 0003 Pretoria, South Africa

Abstract:	R. B. Kusner [R. Guy, Amer. Math. Monthly 90, 196-199 (1983)]asked whether a set of vectors in ${mathbb R}^{d}$ such that thedistance between any pair is 1, has cardinality at mostd + 1.We show that this is true for p = 4and any , and false for all 1d sufficiently large, depending on p. Moregenerally we show that the maximum cardinality is at most if p is an even integer, and at least if 1depends on p.Received: 5 May 2003

Keywords:	Primary 52C10 Secondary 52A21 46B20.
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