Generalized Descents and Normality

2007/09/27 by Miklós Bóna, Miklos Bona, Bona, Miklos
Computer Science · Mathematics · #05A16 #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #math.CO #math.PR #msc:05A16

paper · pdf · doi:10.48550/arxiv.0709.4483

7 pages

arxiv created 2007/09/27 · openalex publication_date 2007/09/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use Janson's dependency criterion to prove that the distribution of d-descents of permutations of length n converge to a normal distribution as n goes to infinity. We show that this remains true even if d is allowed to grow with n, up to a certain degree.

Related

• Limit Theorems for Descents in Permutations and Arithmetic Progressions in ℤ/pℤ
• Classifying Descents According to Parity
• Martingales and descent statistics
• Sharp analysis on the joint distribution of the number of descents and inverse descents in a random permutation
• Central limit theorem for descents in conjugacy classes of S_n