Saturated configuration and new large construction of equiangular lines
Saturated configuration and new large construction of equiangular lines
复制标题
等角线的饱和构型和新型大结构
DOI：
10.1016/j.laa.2019.12.002
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发表时间：
2018
影响因子：
1.1
通讯作者：
Wei
中科院分区：
文献类型：
--
作者：
Y. R. Lin;Wei
在欧几里得空间中，一组通过原点的直线称为等角，当这组直线中的任何一对直线以一个共同的角度相交时。我们研究了欧氏空间中的等角线的最大尺寸，并使用图论的方法来证明，所有目前已知的最大等角线在RD的建设不能添加任何更多的线，以形成一个更大的等角线集时，d= 14，16，17，18，19，和20。给出了R42中248条等角线、R41中200条等角线、R40中168条等角线、R39中152条1/7角等角线和R18中56条1/5角等角线的新构造。
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 R 42, 200 equiangular lines in R 41, 168 equiangular lines in R 40, 152 equiangular lines in R 39 with angle 1/7, and 56 equiangular lines in R 18 with angle 1/5.