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

Vítor H. Fernandes

paper

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

arXiv:2407.05084

Abstract

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.