Abstract

RANK OF SEMIGROUP OF FULL ORDER-PRESERVING CONTRACTION MAPS OF A FINITE CHAIN

Imam, A. T. & Balarabe, M.

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Abstract Let Xn = {1,2,...,n} with its natural order and let T_n be the full transformation semigroup on Xn. A map ? ? T_n is said to be order-preserving if, for all x,y ? Xn, x ? y ? x? ? y?. The map ? ? T_n is said to be a contraction if, for all x,y ? Xn, |x? ?y?| ? |x ?y|. Let ?OCT?_n denote the subsemigroups of all order-preserving contraction maps in T_n. In this paper we computed the rank of ?OCT?_n that is, the smallest number of elements required to generate ?OCT?_n. Keywords: Full transformation, Order-preserving, Contraction, Rank

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