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arXiv · 1403.2155

Equiangular lines in Euclidean spaces

G. Greaves·J. H. Koolen·A. Munemasa·F. Szöllősi
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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.

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G. Greaves, J. H. Koolen, A. Munemasa, F. Szöllősi. 2014-03-10. Equiangular lines in Euclidean spaces. https://doi.org/10.1016/j.jcta.2015.09.008

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