Equiangular lines and the Lemmens–Seidel conjecture

Yen Chi Roger Lin; Wei Hsuan Yu

doi:10.1016/j.disc.2019.111667

Equiangular lines and the Lemmens–Seidel conjecture

Yen Chi Roger Lin, Wei Hsuan Yu^*

^*Corresponding author for this work

Department of Mathematics

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

6 Citations (Scopus)

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 R^r, 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 language	English
Article number	111667
Journal	Discrete Mathematics
Volume	343
Issue number	2
DOIs	https://doi.org/10.1016/j.disc.2019.111667
Publication status	Published - 2020 Feb

Keywords

Equiangular set
Lemmens–Seidel
Pillar methods

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

Access to Document

10.1016/j.disc.2019.111667

Cite this

@article{d912c110f56c4d9e90f3f35d9fc5003e,

title = "Equiangular lines and the Lemmens–Seidel conjecture",

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.",

keywords = "Equiangular set, Lemmens–Seidel, Pillar methods",

author = "Lin, {Yen Chi Roger} and Yu, {Wei Hsuan}",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

year = "2020",

month = feb,

doi = "10.1016/j.disc.2019.111667",

language = "English",

volume = "343",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier BV",

number = "2",

}

TY - JOUR

T1 - Equiangular lines and the Lemmens–Seidel conjecture

AU - Lin, Yen Chi Roger

AU - Yu, Wei Hsuan

PY - 2020/2

Y1 - 2020/2

N2 - 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.

AB - 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.

KW - Equiangular set

KW - Lemmens–Seidel

KW - Pillar methods

UR - http://www.scopus.com/inward/record.url?scp=85072609684&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072609684&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2019.111667

DO - 10.1016/j.disc.2019.111667

M3 - Article

AN - SCOPUS:85072609684

SN - 0012-365X

VL - 343

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 2

M1 - 111667

ER -

Equiangular lines and the Lemmens–Seidel conjecture

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this