Simsun permutations, simsun successions and simsun patterns

2016/02/29 by Shi-Mei Ma, Ma, Shi-Mei, Yeong‐Nan Yeh +2
Mathematics · #05A05 #05A19 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #math.CO #msc:05A05 #msc:05A19

paper · pdf · doi:10.48550/arxiv.1602.08999

11 pages

arxiv created 2016/02/29 · openalex publication_date 2016/02/29 · arxiv updated 2016/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce the definitions of simsun succession, simsun cycle succession and simsun pattern. In particular, the ordinary simsun permutations are permutations avoiding simsun pattern 321. We study the descent and peak statistics on permutations avoiding simsun successions. We give a combinatorial interpretation of the q-Eulerian polynomials introduced by Brenti (J. Combin. Theory Ser. A 91 (2000), 137-170). We also present a bijection between permutations avoiding simsun pattern 132 and set partitions.

Related

• The peak statistics on simsun permutations
• Restricted simsun permutations
• The descent statistic on signed simsun permutations
• On Simsun and Double Simsun Permutations Avoiding a Pattern of Length Three
• Inverse descent statistic for André and simsun permutations