Poisson approximations of the number of fixed points in random multiset permutations

Dudley Stark

Poisson approximations of the number of fixed points in random multiset permutations

Combinatorics 2026-08-01 v1 Probability

Authors: Dudley Stark

Abstract

For ordinary permutations on $n$ letters, the distribution of the number of fixed points of a random permutation is well known to approach the Poisson $(1)$ distribution in total variation distance as $n\to\infty$ . We use Stein's method to get related results for the number of fixed points of random permutations of multisets.

Keywords

Poisson approximation random multiset permutation fixed point Stein's method total variation distance

Cite

@article{arxiv.2608.00710,
  title  = {Poisson approximations of the number of fixed points in random multiset permutations},
  author = {Dudley Stark},
  journal= {arXiv preprint arXiv:2608.00710},
  year   = {2026}
}

Comments

12 pages