The Monoid Rank and Monoid Presentation of Order-Preserving and Order-Decreasing Full Contraction Mappings

Let $n \in \mathbb{Z}^{+}$ and $X_{n}=\{1,2,\ldots,n\}$ be a finite set. $\mathcal ODCT_{n}$ the order-preserving order-decreasing full contraction mappings on $X_{n}$. It is well known that monoid. In this paper, we have found monoid rank presentation of ODCT_{n}$. particular, proved $n-1$ for $$ \geq 3$.