On the combinatorial and rank properties of certain subsemigroups of full contractions of a finite chain

Muhammad Mansur Zubairu, Abdullahi Umar, Muhammad Jada Aliyu

Let $[n]=\{1,2,\dots ,n\}$ be a finite chain and let ${\mathcal{C}\mathcal{T}}_n$ be the semigroup of full contractions on $[n]$. Denote ${\mathcal{O}\mathcal{R}\mathcal{C}\mathcal{T}}_n$ and ${\mathcal{O}\mathcal{C}\mathcal{T}}_n$ to be th…