Enumerations for Permutations by Circular Peak Sets

2008/06/03 by Pierre Bouchard, Bouchard, Pierre, Hungyung Chang +5
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #math.CO #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0806.0435

openalex publication_date 2008/06/03 · arxiv created 2008/06/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The circular peak set of a permutation σ is the set \σ(i)| σ(i-1)<σ(i)>σ(i+1)\. In this paper, we focus on the enumeration problems for permutations by circular peak sets. Let cp_n(S) denote the number of the permutations of order n which have the circular peak set S. For the case with |S|=0,1,2, we derive the explicit formulas for cp_n(S). We also obtain some recurrence relations for the sequence cp_n(S) and give the formula for cp_n(S) in the general case.

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