Number of Several Special Mapping on [1,n] Set
YU Gui-dong · Journal of Kunming University of Science and Technology · 2008
The k-th idempotent mapping on the set [1,n] is firstly defined in this paper,the counting formula of which is obtained by circulating decomposition of permutation groups.The definitions of small preserving mapping and connected image mapping are given afterwards together with their counting formula,a relational formula of the second stirling numbers and the trend of exponential generating function coefficient of the total amount of small preserving mapping.The concepts of alternative mapping as well as top and bottom permutation are also made clear.The concise expression of exponential generating function of top and bottom permutation is finally proved simply.