Ross G. Pinsky

collaborators

4 papers

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

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)}…

math.CO2024

Longest subsequence for certain repeated up/down patterns in random permutations avoiding a pattern of length three

Ross G. Pinsky

Let $S_{n}$ denote the set of permutations of $[n]$ and let $σ = σ_{1} \dots σ_{n} \in S_{n}$ . For a subsequence ${σ_{i_{j}}}_{j = 1}^{k}$ of ${σ_{i}}_{i = 1}^{n}$ of length $k \geq 2$ , construct the ``u…