A note on “Largest independent sets of certain regular subgraphs of the derangement graph”

IF 0.6 3区数学 Q3 MATHEMATICS Journal of Algebraic Combinatorics Pub Date : 2024-02-23 DOI:10.1007/s10801-024-01304-3

Yuval Filmus, Nathan Lindzey

引用次数: 0

Abstract

Let $D_{n,k}$ be the set of all permutations of the symmetric group $S_n$ that have no cycles of length i for all $1 \le i \le k$. In the paper mentioned above, Ku, Lau, and Wong prove that the set of all the largest independent sets of the Cayley graph $\text {Cay}(S_n,D_{n,k})$ is equal to the set of all the largest independent sets in the derangement graph $\text {Cay}(S_n,D_{n,1})$, provided n is sufficiently large in terms of k. We give a simpler proof that holds for all n, k and also applies to the alternating group.

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关于 "错乱图的某些规则子图的最大独立集 "的说明

让 $D_{n,k}$ 是对称组 $S_n$ 的所有排列的集合，这些排列在所有 $1 \le i \le k$ 条件下都没有长度为 i 的循环。在上面提到的论文中，Ku、Lau 和 Wong 证明，只要 n 对 k 来说足够大，那么 Cayley 图 $\text {Cay}(S_n,D_{n,k})$ 中所有最大独立集的集合等于 derangement 图 $\text {Cay}(S_n,D_{n,1})$ 中所有最大独立集的集合。我们给出了一个更简单的证明，它对所有 n、k 都成立，并且同样适用于交替群。

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

Journal of Algebraic Combinatorics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Algebraic Combinatorics provides a single forum for papers on algebraic combinatorics which, at present, are distributed throughout a number of journals. Within the last decade or so, algebraic combinatorics has evolved into a mature, established and identifiable area of mathematics. Research contributions in the field are increasingly seen to have substantial links with other areas of mathematics. The journal publishes papers in which combinatorics and algebra interact in a significant and interesting fashion. This interaction might occur through the study of combinatorial structures using algebraic methods, or the application of combinatorial methods to algebraic problems.

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