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^*

^*此作品的通信作者

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

8 引文斯高帕斯（Scopus）

摘要

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.

原文	英語
文章編號	111667
期刊	Discrete Mathematics
卷	343
發行號	2
DOIs	https://doi.org/10.1016/j.disc.2019.111667
出版狀態	已發佈 - 2020 2月

ASJC Scopus subject areas

理論電腦科學
離散數學和組合

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10.1016/j.disc.2019.111667

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

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AU - Yu, Wei Hsuan

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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

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JO - Discrete Mathematics

JF - Discrete Mathematics

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ER -

Equiangular lines and the Lemmens–Seidel conjecture

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