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We find bivariate generating functions for the $k=1$ cases of recentlyconjectured colored partition identities of Capparelli, Meurman, A. Primc, andM. Primc that are slight variants of the generating functions for the sum sidesof the Andrews-Gordon and Andrews-Bressoud identities. As a consequence, weprove sum-to-product identities for these cases, thus proving the conjectures.

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