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arXiv · 2306.16251

Companions to the Andrews-Gordon and Andrews-Bressoud Identities and Recent Conjectures of Capparelli, Meurman, Primc, and Primc

Matthew C. Russell
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Abstract

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, relating them to recent work of Warnaar. This $k=1$ cases turn out to be equivalent to identities of Jing, Misra, and Savage. Finally, we provide bijections for these identities involving two-rowed cylindric partitions, in the spirit of Corteel.

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Matthew C. Russell. 2023-06-28. Companions to the Andrews-Gordon and Andrews-Bressoud Identities and Recent Conjectures of Capparelli, Meurman, Primc, and Primc. https://doi.org/10.3842/sigma.2026.046

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