Asymptotic analysis of the cyclic structure of permutations

2016/11/09 by Petuchovas, Robertas
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1611.02934

Abstract

This is my dissertation. Its research object is a symmetric group of permutations acting on a finite set. The density of permutations with a given cycle structure pattern is explored when the group order tends to infinity. New and sharper asymptotic formulas are obtained. The latter are applied in approximations of the cycle vector distribution of a random permutation. The saddle-point method, Lagrange-Bürmann inversion formula, Laplace transformations, and other techniques of complex analysis are applied.

Related

• Recent results on permutations without short cycles
• On averages of randomized class functions on the symmetric groups and their asymptotics
• The Cycle Structure of Permutations Without Long Cycles
• Local probabilities for random permutations without long cycles
• Central limit theorem for peaks of a random permutation in a fixed conjugacy class of S_n