Equiangular lines in Euclidean spaces

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:138

Article

Greaves, Gary¹  Koolen, Jacobus H.²  Munemasa, Akihiro¹  Szoellosi, Ferenc¹ 

[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

关键词: Equiangular lines;    Seidel matrix;    Switching;    Two-graph;   

DOI  :  10.1016/j.jcta.2015.09.008

来源: Elsevier

【 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.

【 授权许可】

Free