Browsing by Author "Ibrahim, G. R., Lawal, O. J., Akinwunmi, S. A., Bakare, G. N. & Adeshola A. D."

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    Some Combinatorial Results on Star-Like Transformation Semigroup T αωn∗
    (Mathematical Association of Nigeria, 2022-03-25) Ibrahim, G. R., Lawal, O. J., Akinwunmi, S. A., Bakare, G. N. & Adeshola A. D.
    Let Xn be a finite set and star-like full transformation semi group T αωn∗ be a semigroup of Full Transformation semigroupTn of Xn. Let Height of α∗ be H+(α∗) = | Imα∗|, Fixed point of α∗ be F(α∗) = | {x ∈ X : xα∗ = x} |, Idem potent 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 αωn∗ were character ized 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.