有限集上的划分与置换

Partition and Permutation of a Finite Set

有限集的划分计数问题可通过第二类Stirling数给出解答.在本文中,考虑到有限集的一个划分与置换群Sn中对应的一些置换分解为不相交循环的乘积两者之间是有联系的,本文通过它们之间的联系,得到了第二类Stirling数的一个表达式,从而得到了有限集划分计数问题的又一个表示式.

The problem of the partition of a finite set can be solved by Stirling number of the second kind. In this paper, I find a expression of Stirling number of the second kind by considering the relation between a partition of a finite set and some permutations can reduce the product of disconnect cycles, and obtained another expression of the partition of a finite set.