COMBINATORIAL RESULTS AND GREEN'S RELATION OF STAR-LIKE FULL TRANSFORMATION SEMIGROUPS

Abstract

  be a distinct non negative integer and star-like full transformation semigroup

be a semigroup of Full Transformation semigroup  of . Let Height of α∗ be  = | 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 ∈ | and Relapse of (α∗) be |n −((α∗))|, Green’s relation of semigroup  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 (α∗), J∗(α∗), E | q∗(α∗) | , α∗) , (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. The star-like operator | |≤| Kn − λ Kn+1 | was used to generate some tables of results from the star-like element