Jehanne Dousse
Published 2018-11-06Version 1
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.
Combinatorial proofs of several partition identities of Andrews and Merca
Generalisations of Capparelli's and Primc's identities, I: coloured Frobenius partitions and combinatorial proofs
Partition Identities and the Coin Exchange Problem
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