$q$-Trinomial identities

Details $q$-Trinomial identities $q$-Trinomial identities

1998-10-05

arxiv.org/abs/math/9810018v1

Mathematics

Quantum Algebra

21 pages, AMSLatex

Scientific paper

10.1063/1.532880

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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