Equiangular lines and the Lemmens–Seidel conjecture

Yen Chi Roger Lin, Wei Hsuan Yu

Research output: Contribution to journalArticle

Abstract

In this paper, claims by Lemmens and Seidel in 1973 about equiangular sets of lines with angle 1∕5 are proved by carefully analyzing pillar decomposition, with the aid of the uniqueness of two-graphs on 276 vertices. The Neumann Theorem is generalized in the sense that if there are more than 2r−2 equiangular lines in Rr, 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 r-dimensional Euclidean space for r=8, 9, and 10.

Original languageEnglish
Article number111667
JournalDiscrete Mathematics
Volume343
Issue number2
DOIs
Publication statusPublished - 2020 Feb

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Keywords

  • Equiangular set
  • Lemmens–Seidel
  • Pillar methods

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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