Proofs and reductions of various conjectured partition identities of Kanade and Russell

DOI10.1515/crelle-2019-0012zbMath1447.05023arXiv1809.06089OpenAlexW2949719185WikidataQ113741157 ScholiaQ113741157MaRDI QIDQ2195136

Kathrin Bringmann, Karl Mahlburg, Chris Jennings-Shaffer

Publication date: 7 September 2020

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.06089

zbMATH Keywords

\(q\)-seriesRogers-Ramanujan identitiesinteger partitions

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Partition identities; identities of Rogers-Ramanujan type (11P84)

Related Items (16)

Weighted words at degree two. II: Flat partitions, regular partitions, and application to level one perfect crystals ⋮ Interview with George E. Andrews ⋮ Linked partition ideals and kanade-Russell conjectures ⋮ Asymmetric Rogers–Ramanujan type identities. I. The Andrews–Uncu conjecture ⋮ New proofs of some double sum Rogers-Ramanujan type identities ⋮ Principal subspaces of basic modules for twisted affine Lie algebras, \(q\)-series multisums, and Nandi's identities ⋮ Linked partition ideals and a family of quadruple summations ⋮ Proofs of some partition identities conjectured by Kanade and Russell ⋮ Some more identities of Kanade-Russell type derived using Rosengren's method ⋮ Multi-sum Rogers-Ramanujan type identities ⋮ Partition Inequalities and Applications to Sum-Product Conjectures of Kanade-Russell ⋮ \texttt{qFunctions} -- a Mathematica package for \(q\)-series and partition theory applications ⋮ Andrews-Gordon type series for Kanade-Russell conjectures ⋮ 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 ⋮ New partition identities from \(C^{(1)}_\ell\)-modules

Uses Software

• IdentityFinder

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type
• Ramanujan-Slater type identities related to the moduli 18 and 24
• The structure of standard modules. I: Universal algebras and the Rogers- Ramanujan identities
• The structure of standard modules. II: The case \(A_ 1^{(1)}\), principal gradation
• Infinite-dimensional Lie algebras, theta functions and modular forms
• Annihilating ideals of standard modules of \({\mathfrak sl}(2,{\mathbb{C}})^\sim\) and combinatorial identities
• A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities
• Lie algebraic approaches to classical partition identities
• Construction of the affine Lie algebra \(A^{(1)}_1\)
• Structure of certain level 2 standard modules for \(A_5^{(2)}\) and the Göllnitz-Gordon identities
• Andrews-Gordon type series for Kanade-Russell conjectures
• IdentityFinder and Some New Identities of Rogers–Ramanujan Type
• A Combinatorial Generalization of the Rogers-Ramanujan Identities
• Analytic and combinatorial generalizations of the Rogers-Ramanujan identities
• A new family of algebras underlying the Rogers-Ramanujan identities and generalizations
• Coding the principal character formula for affine Kac-Moody lie algebras
• A Construction of the Level 3 Modules for the Affine Lie Algebra 𝐴₂⁽²⁾ and a New Combinatorial Identity of the Rogers-Ramanujan Type
• Generalizations of Capparelli's identity
• An Analytic Proof of the Rogers-Ramanujan-Gordon Identities
• Partitionen mit Differenzenbedingungen.
• A New Proof of Rogers's Transformations of Infinite Series
• Further Identities of the Rogers-Ramanujan Type

This page was built for publication: Proofs and reductions of various conjectured partition identities of Kanade and Russell