On partition identities of Capparelli and Primc

Abstract

We show that, up to multiplication by a factor $\frac{1}{(cq;q{)}_{\infty }}$, the weighted words version of Capparelli's identity is a particular case of the weighted words version of Primc's identity. We prove this first using recurrences, and then bijectively. We also give finite versions of both identities.

18 pages v2: corrected typos and other minor changes