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.
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