# $q$-Trinomial identities

Authors
Type
Preprint
Publication Date
Oct 05, 1998
Submission Date
Oct 05, 1998
Identifiers
DOI: 10.1063/1.532880
arXiv ID: math/9810018
Source
arXiv
License
Unknown
External links

## Abstract

We obtain connection coefficients between $q$-binomial and $q$-trinomial coefficients. Using these, one can transform $q$-binomial identities into a $q$-trinomial identities and back again. To demonstrate the usefulness of this procedure we rederive some known trinomial identities related to partition theory and prove many of the conjectures of Berkovich, McCoy and Pearce, which have recently arisen in their study of the $\phi_{2,1}$ and $\phi_{1,5}$ perturbations of minimal conformal field theory.

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