Pinnacle sets revisited

2021/06/09 by Justine Falque, Falque, Justine, Jean-Christophe Novelli +3 · 1 citation
Mathematics · #05A05 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2106.05248

openalex publication_date 2021/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 2017, Davis, Nelson, Petersen, and Tenner [Discrete Math. 341 (2018),3249--3270] initiated the combinatorics of pinnacles in permutations. We provide a simple and efficient recursion to compute p_n(S), the number of permutations of S_n with pinnacle set S, and a conjectural closed formula for the related numbers q_n(S). We determine the lexicographically minimal elements of the orbits of the modified Foata-Strehl action, prove that these elements form a lower ideal of the left weak order and characterize and count the maximal elements of this ideal.

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• Pinnacles for Complex Reflection Groups

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