The most frequent peak set of a random permutation

2012/10/22 by Anisse Kasraoui, Kasraoui, Anisse
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1210.5869

openalex publication_date 2012/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a subset S⊆ℙ, let \Pa(S;n) be the number of permutations in the symmetric group of 1,2,...,n that have peak set S. We prove a recent conjecture due to Billey, Burdzy and Sagan, which determines the sets that maximize \Pa(S;n), where S ranges over all subsets of 1,2,...,n.

Related

• Permutations with given peak set
• The pinnacle set of a permutation
• Number of permutations with same peak set for signed permutations
• Central limit theorem for peaks of a random permutation in a fixed conjugacy class of S_n
• Metrics on permutations with the same peak set