Fixed points of non-uniform permutations and representation theory of the symmetric group
Combinatorics
2024-06-28 v2 Probability
Representation Theory
Abstract
We use representation theory of the symmetric group S_n to prove Poisson limit theorems for the distribution of fixed points for three types of non-uniform permutations. First, we give results for the commutator of g and x where g and x are uniform in S_n. Second, we give results for the commutator of g and x where g in uniform in S_n and x is fixed. Third, we give results for permutations obtained by multiplying n*log(n)/i + cn many random i-cycles. Some of our results are known by other, quite different, methods.
Keywords
Cite
@article{arxiv.2406.12139,
title = {Fixed points of non-uniform permutations and representation theory of the symmetric group},
author = {Jason Fulman},
journal= {arXiv preprint arXiv:2406.12139},
year = {2024}
}
Comments
16 pages.This is a major rewriting. Thanks to Jimmy He a conjecture from the previous draft is proved. We also incorporate feedback from Alex Miller