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$q$-Trinomial identities

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Type
Preprint
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Submission Date
Identifiers
DOI: 10.1063/1.532880
arXiv ID: math/9810018
Source
arXiv
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Unknown
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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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