On simplifications of certain \(q\)-multisums

DOI10.1016/j.aam.2006.06.001zbMath1120.33016arXiv1812.05546OpenAlexW2055510794MaRDI QIDQ2370832

Andrew V. Sills

Publication date: 29 June 2007

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.05546

zbMATH Keywords

\(q\)-seriescombinatorial identitiesRogers-Ramanujan identitiesbasic hypergeometric seriesAndrews-Gordon identities

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Cites Work

• A generalization of the Rogers-Ramanujan identities for all moduli
• Generalizations of the Andrews-Bressoud identities for the \(N = 1\) superconformal model \(SM(2, 4\nu )\)
• Rogers-Ramanujan identities: A century of progress from mathematics to physics
• Transformations between basic hypergeometric series on different bases and identities of Rogers-Ramanujan type
• The Andrews-Gordon identities and \(q\)-multinomial coefficients
• Bailey flows and Bose-Fermi identities for the conformal coset models \((A^{(1)}_1)_N\times (A^{(1)}_1)_{N^\prime}/ (A^{(1)}_1)_{N+N^\prime{}}\)
• Rogers-Schur-Ramanujan type identities for the \(M(p,p')\) minimal models of conformal field theory
• The generalized Borwein conjecture. II: Refined \(q\)-trinomial coefficients
• On a hypergeometric identity of Gelfand, Graev and Retakh.
• Polynomial identities, indices, and duality for the \(N=1\) superconformal model \(SM(2,4\nu)\).
• A Combinatorial Generalization of the Rogers-Ramanujan Identities
• Analytic and combinatorial generalizations of the Rogers-Ramanujan identities
• An Analytic Generalization of the Rogers-Ramanujan Identities for Odd Moduli
• Identities of the Rogers-Ramanujan Type
• Some Identities in Combinatory Analysis
• Further Identities of the Rogers-Ramanujan Type
• On identities of the Rogers-Ramanujan type
• The perturbation \(\varphi_{2,1}\) of the \(M(p,p+1)\) models of conformal field theory and related polynomial-character identities
• Change of base in Bailey pairs
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