Saturated configuration and new large construction of equiangular lines

Yen chi Roger Lin; Wei Hsuan Yu

doi:10.1016/j.laa.2019.12.002

Saturated configuration and new large construction of equiangular lines

Yen chi Roger Lin^*, Wei Hsuan Yu

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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 R^d 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 language	English
Pages (from-to)	272-281
Number of pages	10
Journal	Linear Algebra and Its Applications
Volume	588
DOIs	https://doi.org/10.1016/j.laa.2019.12.002
Publication status	Published - 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

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10.1016/j.laa.2019.12.002

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title = "Saturated configuration and new large construction of equiangular lines",

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.",

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AU - Lin, Yen chi Roger

AU - Yu, Wei Hsuan

PY - 2020/3/1

Y1 - 2020/3/1

N2 - 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.

AB - 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.

KW - Clique number

KW - Equiangular lines

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ER -

Saturated configuration and new large construction of equiangular lines

Abstract

Keywords

ASJC Scopus subject areas

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