Abstract

On Cardinality in Finite Semigroup of Full Order -Preserving Contractions

Shamsuddeen Habibu, Umar Mallam Abdulkarim (PhD), H.K Oduwole (PhD), Ibrahim Yusuf Kakangi and Jaiyeola Olorunshola Braimoh

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Abstract In this work, we considered the semi-group OCTn consisting of all mappings of a finite set Xn = {1, 2, 3, - - - , n} which are both order – preserving and contraction, that is mapping ???? ??? such that, for all x ,? ???,? ?? ?? ? ?? ?,??? | ? ? ? ? ? |?| ???| . In particular, we established a closed form formula for the number of elements in OCTn Keyword: Full Transformation, Contraction, Semi-group, order preserving

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