The range of the des statistic for conjugacy classes in S_n

2025/05/28 by Yisca Kares, Kares, Yisca
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2505.22828

openalex publication_date 2025/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Permutation Statistics in Conjugacy Classes of the Symmetric Group
• Central limit theorem for descents in conjugacy classes of S_n
• A note on the Burrows-Wheeler transformation

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