Combinatorics Properties of Order-preserving Full Contraction Transformation Semigroup by Their Equivalence Classes

Abstract

In this paper the cardinalities of equivalence classes of starred Green’s relations in order-preserving full contraction transformation semigroup of a finite set(OCT) and the elements in each equivalence classes were investigated. For each class tables were formed, elements were arrange based on their kernel and image sets, patterns of arrangement observed and formulae were deduced in each case through the combinatorial principles.