Semigroup of transformations with restricted partial range: Regularity, abundance and some combinatorial results

Jiulin Jin, Taijie You

Suppose that $X$ be a nonempty set. Denote by $\mathcal{T}(X)$ the full transformation semigroup on $X$. For $\varnothing \ne Z\subseteq Y\subseteq X$, let $\mathcal{T}(X,Y,Z)=\{α…