Linked partition ideals and Kanade–Russell conjectures

This paper will primarily present a method of proving generating function identities for partitions from linked partition ideals. The method we introduce is built on a conjecture by George Andrews and that those generating functions satisfy some q-difference equations. We will come up with the gener...

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Bibliographic Details
Published in:Discrete mathematics 2020-07, Vol.343 (7), p.111876, Article 111876
Main Authors: Chern, Shane, Li, Zhitai
Format: Article
Language:English
Subjects:
[formula omitted]-difference equations
Computer algebra
Kanade–Russell conjectures
Linked partition ideals
Partitions
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Summary:This paper will primarily present a method of proving generating function identities for partitions from linked partition ideals. The method we introduce is built on a conjecture by George Andrews and that those generating functions satisfy some q-difference equations. We will come up with the generating functions of partitions in the Kanade–Russell conjectures to illustrate the effectiveness of this method.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2020.111876