Equiangular lines in Euclidean spaces
Combinatorics
2016-05-03 v3 Metric Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1403.2155,
title = {Equiangular lines in Euclidean spaces},
author = {G. Greaves and J. H. Koolen and A. Munemasa and F. Szöllősi},
journal= {arXiv preprint arXiv:1403.2155},
year = {2016}
}
Comments
24 pages, to appear in JCTA. Corrected an entry in Table 2