Inversions in Random Permutations Under the Ewens Sampling Distribution With and Without a Prescribed Number of Fixed Points

Ross G. Pinsky, Dominic T. Schickentanz

In the first part of the paper, we study the inversion statistic of random permutations under the family $({\mathbb{P}}_{\theta }^{(n)}{)}_{\theta \ge 0}$ of Ewens sampling distributions on $S_n$. W…