Equiangular lines in Euclidean spaces

被引：51

作者：

Greaves, Gary ^{[1
]}

Koolen, Jacobus H. ^{[2
]}

Munemasa, Akihiro ^{[1
]}

Szoellosi, Ferenc ^{[1
]}

机构：

[1] Tohoku Univ, Grad Sch Informat Sci, Res Ctr Pure & Appl Math, Sendai, Miyagi 9808579, Japan

[2] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2016年 / 138卷

关键词：

Equiangular lines; Seidel matrix; Switching; Two-graph; HADAMARD-MATRICES; EULER GRAPHS; REPRESENTATIONS;

D O I：

10.1016/j.jcta.2015.09.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain several new results contributing to the theory of real equiangular line systems Among other things, we present a new general lower bound on the maximum number of equiangular lines in d dimensional Euclidean space; we describe the two-graphs on 12 vertices; and we investigate Seidel matrices with exactly three distinct eigenvalues. As a result, we improve on two long-standing upper bounds regarding the maximum number of equiangular lines in dimensions d = 14 and d = 16. Additionally, we prove the nonexistence of certain regular graphs with four eigenvalues, and correct some tables from the literature. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：208 / 235

页数：28

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