New Bounds for Spherical Two-Distance Sets
نویسندگان
چکیده
منابع مشابه
New Bounds for Equiangular Lines and Spherical Two-Distance Sets
The set of points in a metric space is called an s-distance set if pairwise distances between these points admit only s distinct values. Two-distance spherical sets with the set of scalar products {α,−α}, α ∈ [0, 1), are called equiangular. The problem of determining the maximal size of s-distance sets in various spaces has a long history in mathematics. We determine a new method of bounding th...
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A set S of unit vectors in n−dimensional Euclidean space is called spherical two-distance set, if there are two numbers a and b so that the inner products of distinct vectors of S are either a or b. The largest cardinality g(n) of spherical two-distance sets does not exceed n(n+3)/2. This upper bound is known to be tight for n = 2, 6, 22. The set of midpoints of the edges of a regular simplex g...
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A two-distance set in E is a point set X in the d-dimensional Euclidean space such that the distances between distinct points in X assume only two different nonzero values. Based on results from classical distance geometry, we develop an algorithm to classify, for a given d, all maximal (largest possible) two-distance sets in E. Using this algorithm we have completed the full classification for...
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ژورنال
عنوان ژورنال: Experimental Mathematics
سال: 2013
ISSN: 1058-6458,1944-950X
DOI: 10.1080/10586458.2013.767725