On the average number of cycles in conjugacy class products
Combinatorics
2024-10-23 v2
Abstract
We show that for the product of two fixed point free conjugacy classes, the average number of cycles is always very similar. Specifically, our main result is that for a randomly chosen pair of fixed point free permutations of cycle types and , the average number of cycles in their product is between and , where is the harmonic number.
Keywords
Cite
@article{arxiv.2310.06659,
title = {On the average number of cycles in conjugacy class products},
author = {Jesse Campion Loth and Amarpreet Rattan},
journal= {arXiv preprint arXiv:2310.06659},
year = {2024}
}