Hi,

Denote [n]={1,2,...,n}.

consider the set of all pairs (f,A) ,f is a function from [n] to [n] such that f(A)=A,where A is a proper subset of [n].

consider also the set of all pairs (f,B) such that f is a function from [n] to [n],and B is a subset of [n] such that f maps B into B and [n]\B into [n]\B.

Find a one to one correspondence between the the two sets of pairs.

Thank's in advance.