Equiangular lines in Euclidean spaces
نویسندگان
چکیده
منابع مشابه
Equiangular subspaces in Euclidean spaces
A set of lines through the origin is called equiangular if every pair of lines defines the same angle, and the maximum size of an equiangular set of lines in R was studied extensively for the last 70 years. In this paper, we study analogous questions for k-dimensional subspaces. We discuss natural ways of defining the angle between k-dimensional subspaces and correspondingly study the maximum s...
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A construction is given of 29(d + 1) 2 equiangular lines in Euclidean d-space, when d = 3 · 22t−1 − 1 with t any positive integer. This compares with the well known “absolute” upper bound of 12d(d+ 1) lines in any equiangular set; it is the first known constructive lower bound of order d2 . For background and terminology we refer to Seidel [3]. The standard method for obtaining a system of equi...
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A family of lines through the origin in Euclidean space is called equiangular if any pair of lines defines the same angle. The problem of estimating the maximum cardinality of such a family in R was extensively studied for the last 70 years. Motivated by a question of Lemmens and Seidel from 1973, in this paper we prove that for every fixed angle θ and sufficiently large n there are at most 2n−...
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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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An L-spherical code is a set of Euclidean unit vectors whose pairwise inner products belong to the set L. We show, for a fixed α, β > 0, that the size of any [−1,−β] ∪ {α}-spherical code is at most linear in the dimension. In particular, this bound applies to sets of lines such that every two are at a fixed angle to each another.
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 138 شماره
صفحات -
تاریخ انتشار 2016