Order of the Disparity of Elements in Full Transformation Semigroup

Let α be a transformation from Xn → Xn where Xn = {1, 2, 3. . . n}, a finite set, also let DsTn,DsOn,DsDnandDsCnbe the classes of disparity of elements of full transformation, order preserving, order decreasing, order preserving and decreasing full transformation semigroup respectively. The disparity of elements in full transformation semigroup is defined as |W+(α) − W−(α)| = p where p = {1, 2} , W+(α) = max(Im(α)) and W−(α) =min(Im(α)). This research investigates the order of elements in DsTn and it subsemigroups, DsOn,DsDnandDsCn.The elements in each semigroup were listed, arranged and tables were formed. The general nth term of the sequences were also derived. This research work has an important application in computational algebra and theoretical computer science.