New bounds for equiangular lines and spherical two-distance sets

研究成果: 雜誌貢獻期刊論文同行評審

10 引文 斯高帕斯(Scopus)

摘要

A set of lines in Rn is called equiangular if the angle between each pair of lines is the same. We derive new upper bounds on the cardinality of equiangular lines. Let us denote the maximum cardinality of equiangular lines in Rn with the common angle arccos α by Mα(n). We prove that M1/a (n) ≤ 1/2 (a2 - 2)(a2 - 1) for any n ∈ N in the interval a2 - 2 ≤ n ≤ 3a2 - 16 and a ≥ 3. Moreover, we discuss the relation between equiangular lines and spherical two-distance sets and we obtain the new results on the maximum spherical two-distance sets in Rn up to n ≤ 417.

原文???core.languages.en_GB???
頁(從 - 到)908-917
頁數10
期刊SIAM Journal on Discrete Mathematics
31
發行號2
DOIs
出版狀態已出版 - 2017

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