Highly symmetric lines

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-05-07 DOI:10.1016/j.laa.2025.05.002

Mikhail Ganzhinov

引用次数: 0

Abstract

A generalization of highly symmetric frames is presented by considering also projective stabilizers of frame vectors. This allows construction of highly symmetric line systems and study of highly symmetric frames in a more unified manner. Construction of highly symmetric line systems involves computation of twisted spherical functions associated with finite groups. Further generalizations include definition of highly symmetric systems of subspaces. We give several examples which illustrate our approach including 3 new kissing configurations which improve lower bounds on the kissing number in

d = 10, 11, 14

to 510, 592 and 1932 respectively.

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高度对称线

通过考虑帧向量的射影稳定器，对高度对称帧进行了推广。这允许以更统一的方式构建高度对称的线系统和研究高度对称的框架。高度对称线系统的构造涉及到与有限群相关的扭球函数的计算。进一步的推广包括子空间的高度对称系统的定义。我们给出了几个例子来说明我们的方法，包括3种新的接吻构型，它们分别提高了d=10、11、14到510、592和1932的接吻次数的下界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.