对正整数n的m-分拆的若干注记

Some Notes for the m-partition of Positive Integering n

文[1]给出了正整数n的无序分拆的拓广概念———n的m-分拆,并给出了相应的分拆数p(n,m)的计数公式和一些性质.本文进一步给出了具有k个分部的n的m-分拆数pk(n,m)的生成函数以及它的一种递推关系.同时还指出了文[1]的一个错误.

There is a extensive definition of the unordered partitions of the positive integer n , that is, the m-partition of the positive integering n in [1]. And the author of [1] got the counting formula and the property of the number of this partition p（n, m） . In this paper, we gave the generating function and recursive relation for pk（n, m） ,the number of the m-partition of n with k parts. And we also found an error in [1].