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.

中文翻译：

---

关于 Capparelli 和 Primc 的分区标识

我们表明，直到乘以因子 $\frac{1}{(cq;q)_{\infty}}$，Capparelli 身份的加权词版本是 Primc 身份的加权词版本的特例。我们首先使用递归证明这一点，然后是双射证明。我们还给出了两个恒等式的有限版本。