In the work of Alladi et al. (J Algebra 174:636–658, 1995) the authors provided a generalization of the two Capparelli identities involving certain classes of integer partitions. Inspired by that contribution, in particular as regards the general setting and the tools the authors employed, we obtain new partition identities by identifying further sets of partitions that can be explicitly put into a one-to-one correspondence by the method described in the 1995 paper. As a further result, although of a different nature, we obtain an analytical identity of Rogers–Ramanujan type, involving generating functions, for a class of partition identities already found in that paper and that generalize the first Capparelli identity and include it as a particular case. To achieve this, we apply the same strategy as Kanade and Russell did in a recent paper. This method relies on the use of jagged partitions that can be seen as a more general kind of integer partitions.

在阿拉迪等人的工作中。（J Algebra 174：636-658，1995）作者提供了涉及某些整数分区类的两个Capparelli恒等式的推广。受此贡献的启发，特别是关于作者使用的一般设置和工具，我们通过识别可以通过1995年描述的方法一对一对应地明确划分的其他分区集，获得了新的分区标识。纸。进一步的结果是，尽管具有不同的性质，但我们获得了该文件中已经发现的一类分区身份的罗杰斯-拉曼努詹类型的分析身份，涉及生成函数，该分区身份概括了第一个Capparelli身份并将其包括为案件。为了实现这一目标，我们采用了Kanade和Russell在最近的论文中所采用的相同策略。