On partition identities of Capparelli and Primc

Jehanne Dousse (1, 2, 3)

1 CTN - Combinatoire, théorie des nombres
2 CNRS - Centre National de la Recherche Scientifique
3 ICJ - Institut Camille Jordan

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.

Domaines: Combinatoire [math.CO]; Théorie des nombres [math.NT]; Théorie des représentations [math.RT]

Jehanne Dousse. On partition identities of Capparelli and Primc. Advances in Mathematics, 2020, 370, ⟨10.1016/j.aim.2020.107245⟩. ⟨hal-02096711⟩