The range of the des statistic for conjugacy classes in $S_n$
Combinatorics
2025-05-30 v1
Abstract
We determine the range of the des statistic on every conjugacy class in the symmetric group , prove that the minimum is (except for the identity class), and show that every intermediate value from to the maximum value is attained. We also demonstrate a constructive method to achieve every value in the range and discuss its combinatorial implications.
Cite
@article{arxiv.2505.22828,
title = {The range of the des statistic for conjugacy classes in $S_n$},
author = {Yisca Kares},
journal= {arXiv preprint arXiv:2505.22828},
year = {2025}
}