超平面上 Sn 轨道的分数

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-08-02 DOI:10.1016/j.laa.2024.07.022

Brendan Pawlowski

引用次数: 0

摘要

黄、麦金农和萨特里阿诺猜想，如果有不同的坐标和，那么通过原点的超平面除了包含最多由 . 的坐标置换得到的矢量外，还包含。我们证明了这一猜想。

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The fraction of an Sn-orbit on a hyperplane

Huang, McKinnon, and Satriano conjectured that if $v \in R^{n}$ has distinct coordinates and $n \geq 3$ , then a hyperplane through the origin other than $\sum_{i} x_{i} = 0$ contains at most $2 ⌊ n / 2 ⌋ (n - 2)!$ of the vectors obtained by permuting the coordinates of v. We prove this conjecture.

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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.