IdentityFinder and Some New Identities of Rogers–Ramanujan Type

DOI10.1080/10586458.2015.1015186zbMath1327.11075arXiv1411.5346OpenAlexW2963175216MaRDI QIDQ3194578

Shashank Kanade, Matthew C. Russell

Publication date: 20 October 2015

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.5346

zbMATH Keywords

\(q\)-seriesRogers-Ramanujan identitiesinteger partitions

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial aspects of partitions of integers (05A17) Vertex operators; vertex operator algebras and related structures (17B69) Partition identities; identities of Rogers-Ramanujan type (11P84)

Related Items (25)

Weighted words at degree two. II: Flat partitions, regular partitions, and application to level one perfect crystals ⋮ A complete generalization of Göllnitz's ``big theorem ⋮ 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, directed graphs and \(q\)-multi-summations ⋮ Andrews-Gordon type series for Capparelli's and Göllnitz-Gordon identities ⋮ 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 general class of Schmidt theorems ⋮ Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type ⋮ 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 ⋮ A variant of \texttt{IdentityFinder} and some new identities of Rogers-Ramanujan-MacMahon type ⋮ Systematic Counting of Restricted Partitions ⋮ IdentityFinder ⋮ 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 $A^{(2)}_2$ ⋮ Reflecting (on) the modulo 9 Kanade-Russell (conjectural) identities ⋮ New partition identities from \(C^{(1)}_\ell\)-modules

Uses Software

• Maple

Cites Work

• Rogers-Ramanujan computer searches
• 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
• Annihilating ideals of standard modules of \({\mathfrak sl}(2,{\mathbb{C}})^\sim\) and combinatorial identities
• Roger-Ramanujan type identities for partitions with attached odd parts
• Construction of the affine Lie algebra \(A^{(1)}_1\)
• Rogers-Ramanujan identities in the hard hexagon model
• A motivated proof of Gordon's identities
• Overpartitions, lattice paths, and Rogers-Ramanujan identities
• A new family of algebras underlying the Rogers-Ramanujan identities and generalizations
• A BASIS OF THE BASIC $\mathfrak{sl} ({\bf 3}, {\mathbb C})^~$-MODULE
• A Motivated Proof of the Rogers-Ramanujan Identities

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