On the monoid of order-preserving transformations of a finite chain whose ranges are intervals

In this note we give a presentation for the monoid $I{O}_n$ of all order-preserving transformations of a $n$-chain whose ranges are intervals. We also consider the submonoid $I{O}_n^{-}$ of $I{O}_n$ consisting of order-decreasing transformations, for which we determine the cardinality, the rank and a presentation.