This paper will primarily present a method of proving generating function identities for partitions from linked partition ideals. The method we introduce is built on a conjecture by George Andrews and that those generating functions satisfy some $q$-difference equations. We will come up with the generating functions of partitions in the Kanade--Russell conjectures to illustrate the effectiveness of this method.

中文翻译：

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连接分区理想和 Kanade-Russell 猜想

本文将主要提出一种从链接分区理想证明分区的生成函数恒等式的方法。我们介绍的方法建立在 George Andrews 的猜想之上，并且那些生成函数满足一些 $q$-差分方程。我们将在 Kanade--Russell 猜想中提出分区的生成函数来说明该方法的有效性。