Andrews-Gordon type series for Kanade-Russell conjectures

DOI10.1007/s00026-019-00470-7zbMath1433.05034arXiv1808.01432OpenAlexW2885748054WikidataQ123144358 ScholiaQ123144358MaRDI QIDQ2299141

Kağan Kurşungöz

Publication date: 20 February 2020

Published in: Annals of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.01432

zbMATH Keywords

Andrews-Gordon identitiespartition generating functionKanade-Russell conjectures

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) (q)-calculus and related topics (05A30) Combinatorial aspects of partitions of integers (05A17) Partition identities; identities of Rogers-Ramanujan type (11P84)

Related Items (17)

Polynomial identities implying Capparelli's partition theorems ⋮ Linked partition ideals and kanade-Russell conjectures ⋮ Asymmetric Rogers–Ramanujan type identities. I. The Andrews–Uncu conjecture ⋮ Principal subspaces of basic modules for twisted affine Lie algebras, \(q\)-series multisums, and Nandi's identities ⋮ Linked partition ideals, directed graphs and \(q\)-multi-summations ⋮ Linked partition ideals and a family of quadruple summations ⋮ Proofs and reductions of various conjectured partition identities of Kanade and Russell ⋮ Some more identities of Kanade-Russell type derived using Rosengren's method ⋮ Multi-sum Rogers-Ramanujan type identities ⋮ A polynomial identity implying Schur’s partition theorem ⋮ A general class of Schmidt theorems ⋮ On double sum generating functions in connection with some classical partition theorems ⋮ \texttt{qFunctions} -- a Mathematica package for \(q\)-series and partition theory applications ⋮ Principal subspaces of twisted modules for certain lattice vertex operator algebras ⋮ Andrews-Gordon type series for the level 5 and 7 standard modules of the affine Lie algebra $A^{(2)}_2$ ⋮ Construction of evidently positive series and an alternative construction for a family of partition generating functions due to Kanade and Russell ⋮ Reflecting (on) the modulo 9 Kanade-Russell (conjectural) identities

Uses Software

• IdentityFinder

Cites Work

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• Cluster parity indices of partitions
• Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type
• Parity considerations in Andrews-Gordon identities
• On some representations of twisted affine Lie algebras and combinatorial identities
• Refinements and generalizations of Capparelli's conjecture on partitions
• Proofs and reductions of various conjectured partition identities of Kanade and Russell
• Andrews-Gordon type series for Capparelli's and Göllnitz-Gordon identities
• IdentityFinder and Some New Identities of Rogers–Ramanujan Type
• An Analytic Generalization of the Rogers-Ramanujan Identities for Odd Moduli

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