Companions to the Andrews-Gordon and Andrews-Bressoud identities, and recent conjectures of Capparelli, Meurman, Primc, and Primc

We find bivariate generating functions for the \(k=1\) cases of recently conjectured colored partition identities of Capparelli, Meurman, A. Primc, and M. Primc that are slight variants of the generating functions for the sum sides of the Andrews-Gordon and Andrews-Bressoud identities. As a conseque...

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Bibliographic Details
Published in:arXiv.org 2023-06
Main Author: Russell, Matthew C
Format: Article
Language:English
Subjects:
Bivariate analysis
Online Access:Get full text
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Summary:We find bivariate generating functions for the \(k=1\) cases of recently conjectured colored partition identities of Capparelli, Meurman, A. Primc, and M. Primc that are slight variants of the generating functions for the sum sides of the Andrews-Gordon and Andrews-Bressoud identities. As a consequence, we prove sum-to-product identities for these cases, thus proving the conjectures.
ISSN:2331-8422