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.
Original language | English |
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Pages (from-to) | 208-235 |
Number of pages | 28 |
Journal | Journal of Combinatorial Theory. Series A |
Volume | 138 |
DOIs | |
Publication status | Published - 2016 Feb 1 |
Keywords
- Equiangular lines
- Seidel matrix
- Switching
- Two-graph
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics