Equiangular lines and the Lemmens-Seidel conjecture
Abstract
In this paper, claims by Lemmens and Seidel in 1973 about equiangular sets of lines with angle are proved by carefully analyzing pillar decompositions, with the aid of the uniqueness of two-graphs on vertices. The Neumann Theorem is generalized in the sense that if there are more than equiangular lines in , then the angle is quite restricted. Together with techniques on finding saturated equiangular sets, we determine the maximum size of equiangular sets "exactly" in an -dimensional Euclidean space for , , and .
Cite
@article{arxiv.1807.06249,
title = {Equiangular lines and the Lemmens-Seidel conjecture},
author = {Yen-chi Roger Lin and Wei-Hsuan Yu},
journal= {arXiv preprint arXiv:1807.06249},
year = {2019}
}
Comments
19 pages, 2 figures. The current bounds for maximum cardinalities of equiangular sets in low dimensions has been updated (Table 1). Lemma 4.8 is corrected, and Theorem 5.3 has been improved. The existence of 14 equiangular lines of rank 8 with angle $(2\sqrt{2}-1)/7$ has been shown (Remark after Theorem 5.3)