MacMahon showed that the generating function for partitions into at most k parts can be decomposed into a partial fraction-type sum indexed by the partitions of k. In the present work, a generalization of MacMahon’s result is given, which in turn provides a full combinatorial explanation.

中文翻译：

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麦克马洪部分分数的组合

MacMahon表明，划分为最多k个部分的生成函数可以分解为由k的分区索引的部分分数类型和。在当前的工作中，给出了MacMahon结果的一般化，这反过来又提供了完整的组合说明。