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Cyclic sieving phenomenon on annular noncrossing permutations

2012/10/27 by Jang Soo Kim, Kim, Jang Soo
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1210.7353

12 pages, 3 figures

arxiv created 2012/10/27 · openalex publication_date 2012/10/27 · arxiv updated 2012/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show an instance of the cyclic sieving phenomenon on annular noncrossing permutations with given cycle types. We define annular q-Kreweras numbers, annular q-Narayana numbers, and annular q-Catalan number, all of which are polynomials in q. We then show that these polynomials exhibit the cyclic sieving phenomenon on annular noncrossing permutations. We also show that a sum of annular q-Kreweras numbers becomes an annular q-Narayana number and a sum of q-Narayana numbers becomes an annular q-Catalan number.

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