正整数n的k部绝对m-分拆性质探讨

Discussion on the Property about the Absolute m-partition of Positive Integer n

提出了n的k部绝对m-分拆的概念,运用组合法、分析法、母函数对其进行研究,得到了一些k部绝对m-分拆的性质定理,同时也将无序分拆与有序分拆的探讨引入到n的k部绝对m-分拆中,给出了k部绝对m-分拆的有序分拆与相应的无序分拆的关系以及k部有序绝对m-分拆的分拆数的计算.还指出了〔王立欣,2000〕中的一个错误,并对其进行了更正.

The new concept of absolute m-partion of positive integer n is introduced. Using the methods of combination, analysis and generating function, some properties of the absolute partion are proposed. Meanwhile, the relation of the partions and compositions of the absolute partion is discussed,and the count- ing formulate of the compositions is given. Finally,a mistake in paper [Wang Lixin, 2000] is pointed out and is corrected.