Linked partition ideals, directed graphs and \(q\)-multi-summations

DOI10.37236/9446zbMath1452.11126arXiv1907.06363OpenAlexW3083178079MaRDI QIDQ2194084

Shane Chern

Publication date: 25 August 2020

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.06363

zbMATH Keywords

linked partition ideals\(q\)-differential systems\(q\)-multi-summations

Mathematics Subject Classification ID

Trees (05C05) Combinatorial aspects of partitions of integers (05A17) Directed graphs (digraphs), tournaments (05C20) Partition identities; identities of Rogers-Ramanujan type (11P84) Other basic hypergeometric functions and integrals in several variables (33D70)

Related Items (6)

Linked partition ideals and the Alladi-Schur theorem ⋮ Linked partition ideals and Andrews-Gordon type series for Alladi and Gordon's extension of Schur's identity ⋮ Principal subspaces of basic modules for twisted affine Lie algebras, \(q\)-series multisums, and Nandi's identities ⋮ Bijections, generalizations, and other properties of sequentially congruent partitions ⋮ Linked partition ideals and a family of quadruple summations ⋮ Linked partition ideals and a Schur-type identity of Andrews

Uses Software

• qMultiSum
• qGeneratingFunctions
• qFunctions

Cites Work

• Unnamed Item
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• A motivated proof of Gordon's identities
• Linked partition ideals and kanade-Russell conjectures
• Andrews-Gordon type series for Kanade-Russell conjectures
• A motivated proof of the Göllnitz-Gordon-Andrews identities
• Andrews-Gordon type series for Capparelli's and Göllnitz-Gordon identities
• Some continued fractions of the Rogers-Ramanujan type
• Partition identities
• IdentityFinder and Some New Identities of Rogers–Ramanujan Type
• A Combinatorial Generalization of the Rogers-Ramanujan Identities
• A general theory of identities of the Rogers-Ramanujan type
• Principal subspaces of twisted modules for certain lattice vertex operator algebras
• An Analytic Proof of the Rogers-Ramanujan-Gordon Identities
• Partitionen mit Differenzenbedingungen.

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