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

2001/10/29 by S. Ole Warnaar · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #math.CO #math.QA #msc:05A15 #msc:05A19 #msc:33D15

paper · pdf · doi:10.1016/s0012-365x(03)00047-5

published as Discrete Mathematics 272 (2003), 215-258 · 36 pages, AMS-LaTeX

arxiv created 2001/10/29 · openalex publication_date 2003/03/25 · arxiv updated 2010/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

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.

Citations

• Supersymmetric Analogs of the Gordon-Andrews Identities, and Related TBA Systems
• The WP - Bailey Tree and its Implications
• Change of base in Bailey pairs

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