Central limit theorem for descents in conjugacy classes of S_n

2018/03/28 by Gene B. Kim, Kim, Gene B., Sangchul Lee +1 · 3 citations
Mathematics · #05A05 #05E99 #60F05 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1803.10457

openalex publication_date 2018/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The distribution of descents in fixed conjugacy classes of S_n has been studied, and it is shown that its moments have interesting properties. Fulman proved that the descent numbers of permutations in conjugacy classes with large cycles are asymptotically normal, and Kim proved that the descent numbers of fixed point free involutions are also asymptotically normal. In this paper, we generalize these results to prove a central limit theorem for descent numbers of permutations in any conjugacy class of S_n.

Citations

• Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum

Cited by

• An asymptotic distribution theory for Eulerian recurrences with applications
• The range of the des statistic for conjugacy classes in S_n
• A central limit theorem for descents and major indices in fixed conjugacy classes of S_n

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