A central limit theorem for descents and major indices in fixed conjugacy classes of S_n

2018/11/12 by Gene B. Kim, Kim, Gene B., Sang‐Chul Lee +1
Mathematics · #05A05 (Secondary) #05A15 #60F05 (Primary) 60C05 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1811.04578

openalex publication_date 2018/11/12 · openalex created_date 2018/11/16 · 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. Kim and Lee showed, by using Curtiss' theorem and moment generating functions, how to prove a central limit theorem for descents in arbitrary conjugacy classes of S_n. In this paper, we prove a modified version of Curtiss' theorem to shift the interval of convergence in a more convenient fashion and use this to show that the joint distribution of descents and major indices is asymptotically bivariate normal.

Citations

• Central limit theorem for descents in conjugacy classes of S_n

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