CARDINALITIES OF EQUIVALENCE CLASSES OF STARRED GREEN’S RELATIONS IN ORDER-PRESERVING FULL CONTRACTION TRANSFORMATION SEMIGROUP OF A FINITE SET

ABSTRACT

The cardinalities of equivalence classes of starred Green’s relations in the order-preserving full contraction transformation semigroup of a finite set (OCTn) were explored in this study, as well as the elements in each equivalence class. Tables were created for each class, components were arranged according to their kernel and image sets, patterns of arrangement were identified, and equations were determined using combinatorial principles in each case.

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