Resistance diameters and critical probabilities of Cayley graphs on irreducible complex reflection groups

IF 0.6 3区数学 Q3 MATHEMATICS Journal of Algebraic Combinatorics Pub Date : 2024-02-25 DOI:10.1007/s10801-024-01302-5

Maksim Vaskouski, Hanna Zadarazhniuk

引用次数: 0

Abstract

We consider networks on minimal Cayley graphs of irreducible complex reflection groups G(m, p, n). We show that resistance diameters of these graphs have asymptotic $\Theta (1/n)$ as $n\rightarrow \infty $ under fixed m, p. Non-trivial lower and upper asymptotic bounds for critical probabilities of percolation for there appearing a giant connected component have been obtained.

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不可还原复反射群上 Cayley 图的电阻直径和临界概率

我们考虑了不可还原复反射群 G(m,p,n)的最小 Cayley 图上的网络。我们证明，在固定的 m、p 条件下，这些图的阻力直径具有渐近的 $\Theta (1/n)$ as $n\rightarrow \infty $。

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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