English

Joint Probabilities within Random Permutations

Combinatorics 2022-05-03 v2 Discrete Mathematics Number Theory

Abstract

A celebrated analogy between prime factorizations of integers and cycle decompositions of permutations is explored here. Asymptotic formulas characterizing semismooth numbers (possessing at most several large factors) carry over to random permutations. We offer a survey of practical methods for computing relevant probabilities of a bivariate or trivariate flavor.

Keywords

Cite

@article{arxiv.2203.10826,
  title  = {Joint Probabilities within Random Permutations},
  author = {Steven Finch},
  journal= {arXiv preprint arXiv:2203.10826},
  year   = {2022}
}

Comments

22 pages, 7 figures

R2 v1 2026-06-24T10:20:10.946Z