论文标题
加权圆柱分区
Weighted cylindric partitions
论文作者
论文摘要
最近，Corteel和Welsh概述了一种通过使用生成圆柱分区的函数与硼丁素定理之间的功能关系来找到新的总产品身份的技术。在这里，我们将此框架扩展到包括来自Han和Xiong的作品的非常通用的产品面。在此过程中，我们被指导考虑结构，例如加权圆柱隔板，对称圆柱隔板和加权偏斜双移平面分区。我们证明了一些新的身份，并获得了已知身份的新证明，包括戈尔尼兹·戈登（Göllnitz-Gordon）和小戈尔尼兹（LittleGöllnitz）身份以及安德鲁斯（Andrews and Paule）的一些美丽的施密特型身份。
Recently Corteel and Welsh outlined a technique for finding new sum-product identities by using functional relations between generating functions for cylindric partitions and a theorem of Borodin. Here, we extend this framework to include very general product-sides coming from work of Han and Xiong. In doing so, we are led to consider structures such as weighted cylindric partitions, symmetric cylindric partitions and weighted skew double shifted plane partitions. We prove some new identities and obtain new proofs of known identities, including the Göllnitz-Gordon and Little Göllnitz identities as well as some beautiful Schmidt-type identities of Andrews and Paule.
