Proofs of some partition identities conjectured by Kanade and Russell

DOI10.1007/s11139-021-00389-9zbMath1523.11189arXiv1912.03689OpenAlexW3156099815WikidataQ113900578 ScholiaQ113900578MaRDI QIDQ6158146

Hjalmar Rosengren

Publication date: 31 May 2023

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.03689

zbMATH Keywords

partitionbasic hypergeometric seriesAskey-Wilson polynomialRogers polynomialKanade-Russell identity

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Partition identities; identities of Rogers-Ramanujan type (11P84)

Related Items (9)

Weighted words at degree two. II: Flat partitions, regular partitions, and application to level one perfect crystals ⋮ Interview with George E. Andrews ⋮ 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 ⋮ Some more identities of Kanade-Russell type derived using Rosengren's method ⋮ Specializing Koornwinder polynomials to Macdonald polynomials of type \(B\), \(C\), \(D\) and \(BC\) ⋮ Multi-sum Rogers-Ramanujan type identities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type
• The structure of standard modules. I: Universal algebras and the Rogers- Ramanujan identities
• A q-integral representation of Rogers' q-ultraspherical polynomials and some applications
• A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities
• Asymptotic and generating relations for the q-Jacobi and //\(4Phi_ 3\) polynomials
• On some representations of twisted affine Lie algebras and combinatorial identities
• Lie algebraic approaches to classical partition identities
• New proofs of determinant evaluations related to plane partitions
• Proofs and reductions of various conjectured partition identities of Kanade and Russell
• Andrews-Gordon type series for Capparelli's and Göllnitz-Gordon identities
• Applications of q-Lagrange Inversion to Basic Hypergeometric Series
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• Some Transformations of Basic Hypergeometric Functions. Part II
• Positivity preserving transformations for 𝑞-binomial coefficients
• Generalizations of Capparelli's identity

This page was built for publication: Proofs of some partition identities conjectured by Kanade and Russell