Linked partition ideals and kanade-Russell conjectures

DOI10.1016/j.disc.2020.111876zbMath1440.05021arXiv1809.08655OpenAlexW3010319188WikidataQ123158103 ScholiaQ123158103MaRDI QIDQ2182194

Shane Chern, Zhitai Li

Publication date: 21 May 2020

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

Full work available at URL: https://arxiv.org/abs/1809.08655

zbMATH Keywords

partitionscomputer algebra\(q\)-difference equationsKanade-Russell conjectureslinked partition ideals

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial aspects of partitions of integers (05A17) Elementary theory of partitions (11P81)

Related Items (9)

Linked partition ideals and the Alladi-Schur theorem ⋮ Asymmetric Rogers–Ramanujan type identities. I. The Andrews–Uncu conjecture ⋮ Linked partition ideals and Andrews-Gordon type series for Alladi and Gordon's extension of Schur's identity ⋮ Linked partition ideals and Euclidean billiard partitions ⋮ Bijections, generalizations, and other properties of sequentially congruent partitions ⋮ Linked partition ideals, directed graphs and \(q\)-multi-summations ⋮ Linked partition ideals and a family of quadruple summations ⋮ Linked partition ideals and a Schur-type identity of Andrews ⋮ Andrews-Gordon type series for the level 5 and 7 standard modules of the affine Lie algebra $A^{(2)}_2$

Uses Software

• Mathematica
• qMultiSum

Cites Work

• Unnamed Item
• Unnamed Item
• Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type
• A Mathematica package for \(q\)-holonomic sequences and power series
• \texttt{qMultiSum} -- a package for proving \(q\)-hypergeometric multiple summation identities
• Proofs and reductions of various conjectured partition identities of Kanade and Russell
• Andrews-Gordon type series for Kanade-Russell conjectures
• Partition identities
• IdentityFinder and Some New Identities of Rogers–Ramanujan Type
• A general theory of identities of the Rogers-Ramanujan type

This page was built for publication: Linked partition ideals and kanade-Russell conjectures