On the Order-Reversing Partial one-to-one Transformation Semigroup (IORN)

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

Abstract:

In this paper, we study the subsemigroup of all order-reversing partial one to one transformation . 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 subsemigroup of order-reversing was identified. 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 order-reversing subsemigroup was computed. The combinatorial results for three variable functions for the order-reversing subsemigroup discovered was enumerated using the parameters defined above.

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Pages: 42-45     |    3 View     |    0 Download