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

Ali Kemal Uncu; A. Berkovich

doi:10.48550/arXiv.1810.12048

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

Ali Kemal Uncu, A. Berkovich

Research Institute for Symbolic Computation

Research output: Working paper and reports › Preprint

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.

Original language	English
Pages	1-10
Number of pages	10
DOIs	https://doi.org/10.48550/arXiv.1810.12048
Publication status	Published - 2018

Publication series

Name	arXiv.org
ISSN (Print)	2331-8422

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101009 Geometry
101012 Combinatorics
101013 Mathematical logic
101020 Technical mathematics

JKU Focus areas

Computation in Informatics and Mathematics

Access to Document

10.48550/arXiv.1810.12048

Cite this

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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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AB - 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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