Equiangular lines in Euclidean spaces

Gary Greaves, Jacobus H. Koolen, Akihiro Munemasa, Ferenc Szöllosi

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)


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 languageEnglish
Pages (from-to)208-235
Number of pages28
JournalJournal of Combinatorial Theory. Series A
Publication statusPublished - 2016 Feb 1


  • Equiangular lines
  • Seidel matrix
  • Switching
  • Two-graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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