Refined $q$-Trinomial Coefficients and Two Infinite Hierarchies of $q$-Series Identities
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.
PDF AbstractCategories
Number Theory
Combinatorics
