.png){kind=icon}
返回
Equiangular lines with a fixed angle
.png){kind=icon}
OA
AI
DOI：10.4007/annals.2021.194.3.3.png)
.png){kind=icon}
原文求助.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
Solving a longstanding problem on equiangular lines, we determine, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separated by the given angle. Fix 0 < alpha < 1. Let N-alpha(d) denote the maximum number of lines through the origin in R-d with pairwise common angle arccos alpha. Let k denote the minimum number (if it exists) of vertices in a graph whose adjacency matrix has spectral radius exactly (1 - alpha)/(2 alpha). If k < infinity, then N-alpha(d) = left perpediculark(d - 1)/(k - 1)]right perpendicualr for all sufficiently large d, and otherwise N-alpha(d) = d+o(d). In particular, N1/(2k-1)(d) = laft perpendiculark(d-1)/(k-1)right perpendicular for every integer k >= 2 and all sufficiently large d. A key ingredient is a new result in spectral graph theory: the adjacency matrix of a connected bounded degree graph has sublinear second eigenvalue multiplicity.
Keyword:
equiangular lines
spectral graph theory
eigenvalue multiplicity
期刊
IF:
5.3
论文数:
1.4K
被引数:
1.6W
机构
引用论文
分享收藏Color Removal from Wastewater using a Synthetic High Performance Antifouling GO-CPTMS@Pd-TKHPP/Polyether Sulfone Nanofiltration Membrane采用合成高性能抗污染GO-CPTMS@Pd-TKHPP/聚醚砜纳滤膜处理废水脱色.png)
OAAI
IF0
OAAI分享收藏分享收藏
Crystal Structure of Triphenyl Cyamelurate (2,5,8-Triphenoxy-1,3,4,6,7,9,9b-heptaazaphenalene)HETEROCYCLESOAAI
HETEROCYCLESIF0
OAAI分享收藏Empirical analysis of electromagnetic profiles for groundwater prospecting in rural areas of Ibadan, southwestern Nigeria伊巴丹西南部尼日利亚农村地区地下水勘探中电磁剖面法的实证分析
PREAI
分享收藏
查看更多内容