A computer proof of a polynomial identity implying a partition theorem of Göllnitz

DOI10.1006/aama.2001.0764zbMath1021.11027arXivmath/0102106OpenAlexW2041103088MaRDI QIDQ696795

Axel Riese, Alexander Berkovich

Publication date: 12 September 2002

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

Full work available at URL: https://arxiv.org/abs/math/0102106

zbMATH Keywords

partitions\(q\)-binomial coefficientsGöllnitz's theoremmathematica packageqMultiSum

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83)

Related Items (5)

New polynomial analogues of Jacobi's triple product and Lebesgue's identities ⋮ \(q\)-hypergeometric proofs of polynomial analogues of the triple product identity, Lebesgue's identity and Euler's pentagonal number theorem ⋮ \texttt{qMultiSum} -- a package for proving \(q\)-hypergeometric multiple summation identities ⋮ A Priori Solution Estimates for Nonlinear Vector Integral Equations ⋮ Creative Telescoping for Holonomic Functions

Uses Software

• Mathematica
• qMultiSum

Cites Work

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• An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)) multisum/integral identities
• A quartic key identity for a partition theorem of Göllnitz
• \texttt{qMultiSum} -- a package for proving \(q\)-hypergeometric multiple summation identities
• A double bounded version of Schur's partition theorem
• Partitionen mit Differenzenbedingungen.

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