关于分划中几个结果的推广
Generalization of a few results in Integer Partitions
摘要：
在本文中，我们推广了几个重要的结果，在分划;即结果被称为斯坦利的定理和长老的定理，并提出了由Ramanujan的同余结果的配分函数。我们推广的结果斯坦利和长老从一个固定的整数到一个数组的后续整数，并提出了一个类似的拉马努金的同余关系的“部分数”的功能，而不是分区功能。我们还推导出的“零件数”的生成函数，并通过一个新的使用费雷尔的图表与他们的图形解释的技术成果。
英文摘要：
In this paper, we generalize a few important results in Integer Partitions; namely the results known as Stanley's theorem and Elder's theorem, and the congruence results proposed by Ramanujan for the partition function. We generalize the results of Stanley and Elder from a fixed integer to an array of subsequent integers, and propose an analogue of Ramanujan's congruence relations for the `number of parts' function instead of the partition function. We also deduce the generating function for the `number of parts', and relate the technical results with their graphical interpretations through a novel use of the Ferrer's diagrams.
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