Saturated configuration and new large construction of equiangular lines

Yen chi Roger Lin, Wei Hsuan Yu

Research output: Contribution to journalArticle

Abstract

A set of lines through the origin in Euclidean space is called equiangular when any pair of lines from the set intersects with each other at a common angle. We study the maximum size of equiangular lines in Euclidean space and use a graph theoretic approach to prove that all the currently known constructions for maximum equiangular lines in Rd cannot be added by any more lines to form a larger equiangular set of lines when d=14,16,17,18,19, and 20. We give new constructions of large equiangular lines which are 248 equiangular lines in R42, 200 equiangular lines in R41, 168 equiangular lines in R40, 152 equiangular lines in R39 with angle 1/7, and 56 equiangular lines in R18 with angle 1/5.

Original languageEnglish
Pages (from-to)272-281
Number of pages10
JournalLinear Algebra and Its Applications
Volume588
DOIs
Publication statusPublished - 2020 Mar 1

Keywords

  • Clique number
  • Equiangular lines

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

Fingerprint Dive into the research topics of 'Saturated configuration and new large construction of equiangular lines'. Together they form a unique fingerprint.

  • Cite this