On the Ranks of Semigroup of Order-preserving or Order-reversing Partial Contraction Mappings on a Finite Chain

B. Ali, M. A. Jada, M. M. Zubairu

Let ${\mathcal{C}\mathcal{P}}_n$ be the semigroup of partial contraction mappings on $[n]=\{1,2,\dots ,n\}$ and let ${\mathcal{O}\mathcal{C}\mathcal{P}}_n$ and ${\mathcal{O}\mathcal{R}\mathcal{C}\mathcal{P}}_n$ be its subsemigroups consisting of…