The most frequent peak set of a random permutation

Abstract

Given a subset $S\subseteq \mathbb{P}$, 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 $1,2,...,n$.

References in corpus (1)

• Permutations with given peak set