Saturated configuration and new large construction of equiangular lines

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 cons...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 588; pp. 272 - 281
Main Authors Lin, Yen-chi Roger, Yu, Wei-Hsuan
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.03.2020
American Elsevier Company, Inc
Subjects
Clique number
Equiangular lines
Euclidean geometry
Euclidean space
Linear algebra
05C50
Clique number
Equiangular lines
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Summary: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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2019.12.002