Ferrers图在正整数拆分中的应用

Appliance of Ferrers Graph to the Positive Integer Partition

正整数的拆分与许多计数问题有着密切的关系.文章运用Ferrers图讨论了正整数拆分问题,得到正整数拆分的共轭拆分表达式,证明了正整数进行拆分的拆分数,可转化为求较小数n-m(m+1)/2的拆分数.

The positive integer partition has close relation with many enumeration prob lems. The paper discusses the partitions of positive integer by applying to the Ferrers graph,and conjugate partition expression of the positive integer is obtained. We have proved that the number of the m-partition of the positive integer n can be translated into partitions of the positive integer n-m（m＋1）/2,which is smaller than n.