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

Abstract

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