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Companions to the Andrews-Gordon and Andrews-Bressoud Identities and Recent Conjectures of Capparelli, Meurman, Primc, and Primc
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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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Combinatorial construction of Russell's series for partition classes defined by Capparelli, Meurman, Primc, and Primc in the $k$=1 Case
The paper supplies a base-partition-and-moves combinatorial model for Russell's bivariate generating series of CMPP partitions in the k=1 case and completes several missing cases.
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