In the spirit of Göllnitz’s “big” partition theorem of 1967, we present a new mod-6 partition identity. Alladi et al. provided a four-parameter refinement of Göllnitz’s big theorem in 1995 via a key identity of generating functions and the method of weighted words. By means of this technique, two similar mod-6 identities of this type were discovered—one by Alladi in 1999 and one by Alladi and Andrews in 2015. We finish the picture by presenting and proving the fourth and final possible mod-6 identity in this spirit. Furthermore, we provide a complete generalization of mod-n identities of this type. Finally, we apply a similar argument to generalize an identity of Alladi et al. from 2003.

本着1967年Göllnitz的“大”分区定理的精神，我们提出了一个新的mod-6分区标识。阿拉迪等。通过生成函数的关键标识和加权词的方法，在1995年对Göllnitz大定理进行了四参数改进。通过这种技术，发现了两个类似的这种类型的mod-6身份-一个是由Alladi于1999年提出的，另一个是由Alladi和Andrews在2015年提出的。这种精神。此外，我们还提供国防部-完整概括ň这种类型的身份。最后，我们应用类似的论点来概括Alladi等人的身份。从2003年开始。