In a recent paper (), Erickson and Hunziker consider partitions in which the arm–leg difference is an arbitrary constant . In previous works, these partitions are called -asymmetric partitions. Regarding these partitions and their conjugates as highest weights, they prove an identity yielding an infinite family of dimension equalities between and modules. Their proof proceeds by the manipulations of the hook content formula. We give a simple combinatorial proof of their result.

中文翻译：

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Erickson 和 Hunziker 维度恒等式的简短组合证明

在最近的一篇论文 () 中，Erickson 和 Hunziker 考虑了臂腿差为任意常数 的分区。在以前的工作中，这些分区称为非对称分区。将这些分区及其共轭视为最高权重，它们证明了在 和 模块之间产生无限维数等式的恒等式。他们的证明是通过对钩子内容公式的操作来进行的。我们给出了他们的结果的简单组合证明。