Some Combinatorial Results on Star-Like Transformation Semigroups
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Date
2022-12-01
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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.
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