On the number of cycles in a random permutation

TL;DR

This paper proves that the number of cycles in a permutation drawn from a generalized Ewens measure follows a normal distribution, providing asymptotic estimates for its mean and variance.

Contribution

It extends the understanding of cycle counts in permutations under generalized Ewens measures by establishing normality and deriving asymptotic parameters.

Findings

Number of cycles is normally distributed.

Asymptotic mean and variance are computed.

Results generalize previous models.

Abstract

We show that the number of cycles in a random permutation chosen according to generalized Ewens measure is normally distributed and compute asymptotic estimates for the mean and variance.