正整数分拆中的特殊恒等式

针对正整数有限制的无序分拆,首先给出＂将n分拆成m个最大数是k的分拆数＂所具备的两个相关恒等式,然后又给出＂当n是k的倍数时,将n分拆成k的次方之和的分拆数＂所具有的几个恒等式,并在运用模型分析和母函数对这些恒等式进行分析证明的基础上,进一步举例加以验证.

Some Special Identities about Partitions of Positive Integer

For positive integer split with restricted condition and unorder, first of all give ＂ n will be split into the number of m with the largest number of k ＂has the two related identities, and then given related several identities about ＂When n is a multiple of k, the n will be split into the separations of the power of k ＂. On the basis of analysis and proof these identities by applying to model analysis and generating function, further verify them by examples.