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

We give a presentation for the monoid IOₙ I O n of all order-preserving transformations of an n -chain whose ranges are intervals. We also consider the submonoid IOₙ⁻ I O n - of IOₙ I O n consisting of order-decreasing transformations, for which we determine the cardinality, the rank and a presentation.