$q$-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 ${\varphi }_{2,1}$ and ${\varphi }_{1,5}$ perturbations of minimal conformal field theory.

21 pages, AMSLatex

References in corpus (3)

• A Burge tree of Virasoro-type polynomial identities
• The perturbations ${\varphi }_{2,1}$ and ${\varphi }_{1,5}$ of the minimal models $M(p,p^{\prime })$ and the trinomial analogue of Bailey's lemma
• A Trinomial Analogue of Bailey's Lemma and N=2 Superconformal Invariance

Cited by in corpus (4)

• The generalized Borwein conjecture. II. Refined q-trinomial coefficients
• On identities of the Rogers--Ramanujan type
• Refined q-trinomial coefficients and character identities
• A quartet of fermionic expressions for $M(k,2k\pm 1)$ Virasoro characters via half-lattice paths