Enumeration of permutations by number of cyclic occurrence of peaks and valleys

2012/03/28 by Shi-Mei Ma, Ma, Shi-Mei, Chak-On Chow +1
Computer Science · Mathematics · #05A05 #05A15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1203.6264

openalex publication_date 2012/03/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we focus on the enumeration of permutations by number of cyclic occurrence of peaks and valleys. We find several recurrence relations involving the number of permutations with a prescribed number of cyclic peaks, cyclic valleys, fixed points and cycles. Several associated permutation statistics and the corresponding generating functions are also studied. In particular, we establish a connection between cyclic valleys and Pell numbers as well as cyclic peaks and alternating runs.

Citations

• Valleyless Sequences

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