q-Trinomial identities
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 φ2,1 and φ1,5 perturbations of minimal conformal field theory.
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