The variance of the Stirling cycle numbers

2005/11/17 by Herbert S. Wilf, Wilf, Herbert S.
Mathematics · #05A16 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A16

paper · pdf · doi:10.48550/arxiv.math/0511428

openalex publication_date 2005/11/17 · arxiv created 2005/11/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the probability that two permutations of n letters have the same number of cycles is ∼ \frac12√πlogn.

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• Stirling permutations, cycle structures of permutations and perfect matchings
• Stirling permutation codes
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