English

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 α\alpha and β\beta, the average number of cycles in their product is between Hn3H_n-3 and Hn+1H_n+1, where HnH_n 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}
}