The generalized Borwein conjecture. II. Refined q-trinomial coefficients

Abstract

Transformation formulas for four-parameter refinements of the q-trinomial coefficients are proven. The iterative nature of these transformations allows for the easy derivation of several infinite series of q-trinomial identities, and can be applied to prove many instances of Bressoud's generalized Borwein conjecture.

36 pages, AMS-LaTeX

References in corpus (6)

• 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
• Change of base in Bailey pairs
• $q$-Trinomial identities
• Refined q-trinomial coefficients and character identities
• The WP - Bailey Tree and its Implications

Cited by in corpus (13)

• q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon
• A q-rious positivity
• On identities of the Rogers--Ramanujan type
• An analytic proof of the Borwein Conjecture
• Refined q-trinomial coefficients and character identities
• Races among products
• New path description for the M(k+1,2k+3) models and the dual Z_k graded parafermions
• Parafermionic derivation of Andrews-type multiple sums
• On double sum generating functions in connection with some classical partition theorems
• A partial theta function Borwein conjecture
• On simplifications of certain $q$-multisums
• Extension of Bressoud's generalization of Borwein's conjecture and some exact results
• A new recursion for Bressoud's polynomials