正整数拆分的几个性质

Some Properties on Partitions of Positive Integer

文章运用母函数和Ferrers图像讨论了正整数拆分问题,对Ferrers图像性质进行了扩充,提出了正整数拆分的几个性质,谈论了将正整数n按不同要求进行拆分时所对应的拆分数之间的关系.并对文献[1]的有关正整数拆分的两个定理进行探讨,推广得到了两个新的结论.

The paper discusses the partitions of positive integer by applying to generating function and the Ferrers graphic, which expands some property of Ferrets graphic and puts forward two properties of partitions of positive integer and analyses the relationship between the partition numbers when a positive integer n is split into partitions according to different requirements. In the paper, the author also explores and generalizes two theorems given in reference [ 1 ] and draws two new conclusions.