Counting symmetric and non-symmetric peaks in a set partition

2024/01/03 by Walaa Asakly, Asakly, Walaa, Noor Kezil +1
Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2401.01687

openalex publication_date 2024/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to derive explicit formulas for two distinct values. The first is the total number of symmetric peaks in a set partition of [n] with exactly k blocks, and the second one is the total number of non-symmetric peaks in a set partition of [n] with exactly k blocks. We represent these results in two ways. First by using the theory of generating functions, and the second by using combinatorial tools.

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