A complete generalization of Göllnitz's ``big theorem

DOI10.1007/s11139-020-00262-1zbMath1462.05028OpenAlexW3044622186MaRDI QIDQ829640

Jongwon Kim, Terence Coelho, Matthew C. Russell

Publication date: 6 May 2021

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-020-00262-1

zbMATH Keywords

combinatoricsgenerating functionbijectionpartition theoryRogers-Ramanujan typedistinct partskey-identityproduct-sidesum-sideweighted words

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial aspects of partitions of integers (05A17) Elementary theory of partitions (11P81) Partition identities; identities of Rogers-Ramanujan type (11P84)

Uses Software

• IdentityFinder

Cites Work

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• A variation on a theme of Sylvester -- a smoother road to Göllnitz's (Big) theorem
• Generalizations of Schur's partition theorem
• A new four parameter \(q\)-series identity and its partition implications
• A new bijective proof of a partition theorem of K. Alladi
• The dual of Göllnitz's (big) partition theorem
• A refinement of the Alladi-Schur theorem
• IdentityFinder and Some New Identities of Rogers–Ramanujan Type
• Partitionen mit Differenzenbedingungen.
• On a partition theorem of Göllnitz and related formulae.

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