On Combinatorial Property of Compressive Transformation Semigroup
Taijie You · Journal of Huaiyin Institute of Technology · 2012
Let be transformation semigroup on finite set Xn={1,2,…,n}.For all α∈Tn,we shall call α is compressive element of Tn if|xα-yα|≤|x-y| for all x,y in Xn.Let CTn be a set that consists of the compressive element of Tn.Then CTn is a subsemigroup of Tn,we call CTn as compressive semigroup.It is shown that |CTn|=n·3n-1-2∑n-1j=1LN1j·3n-1-j;LN1n=3LN1n-1-LNn-1(1,1),n≥3;LN(1,1)n=2LN(1,1)n-1+LN(1,321)n,n≥5.