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arXiv · 2505.22828

The range of the des statistic for conjugacy classes in $S_n$

Yisca Kares
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Abstract

We determine the range of the des statistic on every conjugacy class in the symmetric group $S_n$, prove that the minimum is $1$ (except for the identity class), and show that every intermediate value from $1$ to the maximum value is attained. We also demonstrate a constructive method to achieve every value in the range and discuss its combinatorial implications.

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Yisca Kares. 2025-05-28. The range of the des statistic for conjugacy classes in $S_n$. https://arxiv.org/abs/2505.22828

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