Green's relations in finite function semigroups

Let? _n be the set of all partial functions on ann-element setX _n , i.e., the set of all functions whose domain and range are subsets ofX _n . Green's equivalence relations?, ?, ? and? are considered, and the number and cardinality of the corresponding equivalence classes are determined. The number of idempotent and generalized idempotent elements in? _n is also determined.