Abstract:We use representation theory of $S_n$ to analyze the mixing of cycle type statistics $a_j(\sigma) = \{\text{# of $j$-cycles of $\sigma$}\}$ for any fixed $j$ in permutations $\sigma_t$ resulting from the $t$-step random transposition walk on $S_n$. We also derive analogous results for the star transposition walk. Our approach uses the method of moments; a key ingredient is a new formula for the coefficients in the irreducible character decomposition of the $S_n$-class function $(a_j)^r(\sigma)=\{(\text{# of $j$-cycles of $\sigma$})^r\}$ for any positive integers $r,j$ when $n\geq 2rj$.
From: Dominic Arcona [view email]
[v1]
Tue, 16 Dec 2025 00:16:21 UTC (33 KB)
[v2]
Thu, 27 Aug 2026 20:31:50 UTC (51 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。