Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type

zbMath1409.05018arXiv1803.02515MaRDI QIDQ668049

Shashank Kanade, Matthew C. Russell

Publication date: 5 March 2019

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

Full work available at URL: https://arxiv.org/abs/1803.02515

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 (30)

Polynomial identities implying Capparelli's partition theorems ⋮ Sequences, q-Multinomial Identities, Integer Partitions with Kinds, and Generalized Galois Numbers ⋮ Linked partition ideals and kanade-Russell conjectures ⋮ Generalisations of Capparelli's and Primc's identities. I: Coloured Frobenius partitions and combinatorial proofs ⋮ 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 ⋮ 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 ⋮ On the \(q\)-binomial identities involving the Legendre symbol modulo 3 ⋮ A polynomial identity implying Schur’s partition theorem ⋮ New infinite hierarchies of polynomial identities related to the Capparelli partition theorems ⋮ On double sum generating functions in connection with some classical partition theorems ⋮ Partition Inequalities and Applications to Sum-Product Conjectures of Kanade-Russell ⋮ \texttt{qFunctions} -- a Mathematica package for \(q\)-series and partition theory applications ⋮ On partition identities of Capparelli and Primc ⋮ Elementary polynomial identities involving \(q\)-trinomial coefficients ⋮ Andrews-Gordon type series for Kanade-Russell conjectures ⋮ A variant of \texttt{IdentityFinder} and some new identities of Rogers-Ramanujan-MacMahon type ⋮ Refined q-Trinomial Coefficients and Two Infinite Hierarchies of q-Series Identities ⋮ Systematic Counting of Restricted Partitions ⋮ Some partition and analytical identities arising from the Alladi, Andrews, Gordon bijection ⋮ 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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