Central limit theorem for the prefix exchange distance under Ewens sampling formula

被引：1

作者：

Grusea, Simona ^{[1
]}

Labarre, Anthony ^{[2
,3
]}

机构：

[1] Univ Toulouse, Inst Math Toulouse, INSA Toulouse, 135 Ave Rangueil, F-31400 Toulouse, France

[2] Univ Paris Est, LIGM, CNRS, UMR 8049, Champs Sur Marne, France

[3] Univ Paris Est Marne La Vallee, 5 Blvd Descartes, F-77420 Champs Sur Marne, France

来源：

DISCRETE MATHEMATICS | 2021年 / 344卷 / 02期

关键词：

n-star graph; Permutation; Ewens sampling formula; Prefix exchange distance; Feller coupling; Central limit theorem;

D O I：

10.1016/j.disc.2020.112206

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The prefix exchange distance of a permutation is the length of its shortest factorisation into transpositions that all contain 1. Using a probabilistic approach, we obtain expressions for the mean and the variance, and prove the asymptotic normality of the distribution of this distance for a random permutation verifying the Ewens sampling formula. Analogous results in the uniform setting follow as simple corollaries. (c) 2020 Elsevier B.V. All rights reserved.

引用

页数：6

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