Real Zeros and Normal Distribution for statistics on Stirling permutations defined by Gessel and Stanley

2007/08/23 by Miklós Bóna, Miklos Bona, Bona, Miklos · 2 citations
Computer Science · Mathematics · #05A05 #05A15 #05A16 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #math.CO #math.PR #msc:05A05 #msc:05A15 #msc:05A16 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0708.3223

8 pages

openalex publication_date 2007/08/23 · arxiv created 2008/03/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Stirling permutations defined by Gessel and Stanley. We prove that their generating function according to the number of descents has real roots only. We use that fact to prove that the distribution of these descents, and other, equidistributed statistics on these objects converge to a normal distribution.

Cited by

• Symmetric decompositions and Euler-Stirling statistics on Stirling permutations
• Eulerian-type polynomials over Stirling permutations and box sorting algorithm

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