Refined q-Trinomial Coefficients and Two Infinite Hierarchies of q-Series Identities

2018/10/29 by Alexander Bérkovich, Berkovich, Alexander, Ali Kemal Uncu +1
Mathematics · #05A10 #05A15 #05A17 #11B65 #11C08 #11P81 #11P82 #11P83 #11P84 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1810.12048

openalex publication_date 2018/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We will prove an identity involving refined q-trinomial coefficients. We then extend this identity to two infinite families of doubly bounded polynomial identities using transformation properties of the refined q-trinomials in an iterative fashion in the spirit of Bailey chains. One of these two hierarchies contains an identity which is equivalent to Capparelli's first Partition Theorem.

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