Ross G. Pinsky

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math.PR2025

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 $(P_{I^} ¸^{(n)})_{I^¸ \geq 0}$ of Ewens sampling distributions on $S_{n}$ .…

math.PR2025

A family of non-uniform distributions on the set of parking functions generated by random permutations

Ross G. Pinsky

We introduce a rather natural family of non-uniform distributions on $P F_{n}$ , $n \in N$ , the set of parking functions of length $n$ . One of the motivations for this comes fro…

math.PR2025

The inversion statistic in derangements and in other permutations with a prescribed number of fixed points

Ross G. Pinsky

We study how the inversion statistic is influenced by fixed points in a permutation. %The expected number of inversions in a uniformly random permutation in $S_{n}$ is $\frac{n(n-1)}…