Some Combinatorial Problems in Triad Subsemigroups of Symmetric Inverse Semigroup (In)

Author(s): Michael Cornelius, MI Bello, NH Manjak and Ishiaku Zubairu

Abstract:

Let X_n={1,2,3,..,n} and Let α:Domα⊆X_n⟶Im⊆X_n be a partial one-to-one transformation on . The elements of partial one to one transformation semigroup were constructed and a Triad subsemigroup was identified using the intersections of order-preserving, order-reversing and order-decreasing partial one to one transformation subsemigroup. The following parameters are defined: the fix point of , the height of , the positive waist of , the derangement of , the idempotent of and cardinality of the Triad subsemigroup of course other parameters have been defined and many more could be still be defined, but we shall restrict ourselves to only these, in this paper. The combinatorial results for three variable functions for the subsemigroup (Triad) discovered was enumerated using the parameters defined. The results were presented and highlighted open problems.

keywords:

Pages: 37-41     |    3 View     |    0 Download