Euler's partition theorem for all moduli and new companions to Rogers-Ramanujan-Andrews-Gordon identities

DOI10.1007/s11139-018-0103-yzbMath1470.11266arXiv1608.03635OpenAlexW2963730699WikidataQ128287187 ScholiaQ128287187MaRDI QIDQ2319925

Xinhua Xiong, William J. Keith

Publication date: 20 August 2019

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

Full work available at URL: https://arxiv.org/abs/1608.03635

zbMATH Keywords

generating functionspartition identitiesq-seriesEuler's partition theoremRogers-Ramanujan-Andrews-Gordon identities

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83)

Related Items (9)

Weighted words at degree two. II: Flat partitions, regular partitions, and application to level one perfect crystals ⋮ Beck-type identities: new combinatorial proofs and a modular refinement ⋮ A general class of Schmidt theorems ⋮ Unnamed Item ⋮ Beck-type companion identities for Franklin's identity via a modular refinement ⋮ A lecture Hall theorem for \(m\)-falling partitions ⋮ A variant of \texttt{IdentityFinder} and some new identities of Rogers-Ramanujan-MacMahon type ⋮ Euler’s Partition Theorem and Refinements Without Appeal to Infinite Products ⋮ The arithmetical combinatorics of \(k,l\)-regular partitions

Cites Work

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• New weighted partition theorems with the emphasis on the smallest part of partitions
• On generalizations of Euler's partition theorem
• New weighted Rogers-Ramanujan partition theorems and their implications
• An Analytic Proof of the Rogers-Ramanujan-Gordon Identities

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