The absence of a pattern and the number of occurrences of another

2009/10/07 by Miklós Bóna, Bona, Miklos
Computer Science · Mathematics · #05A15 #05A16 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0910.1343

openalex publication_date 2009/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following a question of J. Cooper, we study the expected number of occurrences of a given permutation pattern q in permutations that avoid another given pattern r. In some cases, we find the pattern that occurs least often, (resp. most often) in all r-avoiding permutations. We also prove a few exact enumeration formulae, some of which are surprising.

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