Some Combinatorial Results on Star-Like Transformation Semigroups

Abstract

Let Xn be a nite set and star-like full transformation semi- group T ! n be a semigroup of Full Transformation semigroup Tn of Xn. Let Height of be H+( ) = j Im j, Fixed point of be F( ) = j fx 2 X : x = xg j, Idem- potent of be j F( ) j=j Im j , Collapse of ( ) be j [ft 􀀀1 : t 2 T ! g j and Relapse of ( ) be j n 􀀀 C+(( )) j and also, Green's relation of semigroup T ! n were character- ized using the general method and de nitions.The methods employed in carrying out this research work were that the elements in each of the functions were listed and some tables were formed for H+( ), J ( ), E j q ( ) j , C ( ) , C􀀀( ) and L , R ,D , H and J equivalence relations from these tables, triangular array and sequences were formed; the patterns of the arrangement were studied, formulae were deduced in different cases through the combinatorial principle.