Some Combinatorial Results on Star-Like Transformation Semigroup T αω∗ n

Let Xn be a finite set and star-like full transformation semigroup T αω∗ n be a semigroup of Full Transformation semigroup Tn of Xn. Let Height of α ∗ be H+(α ∗ ) = | Imα∗ |, Fixed point of α ∗ be F(α ∗ ) = | {x ∈ X : xα∗ = x} |, Idempotent of α ∗ be | F(α ∗ ) |=| Imα∗ | , Collapse of (α ∗ ) be | ∪{tα−1 : t ∈ T αω∗} | and Relapse of (α ∗ ) be | n − C +((α ∗ )) | and also, Green’s relation of semigroup T αω∗ n were characterized using the general method and definitions.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+(α ∗ ), J ∗ (α ∗ ), E | q ∗ (α ∗ ) | , C ∗ (α ∗ ) , C −(α ∗ ) 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.