On Cardinality in Finite Semigroup of Full Order-Preserving ContractionsOn Cardinality in Finite Semigroup of Full Order-Preserving Contractions

In this work, we considered the semigroup OCTn consisting of all mappings of a finite set Xn = {1, 2, 3,---- , n} which are both order - preserving and contraction, that is mapping a •• Xn -» Xn such that, for all x ,y E Xnfx- <y => x a <y a, and | x a — y a | < | x — y\ . In particular, we established a closed form formular for the number of elements . in OCTn