Fixed points of orientation-preserving full transformation

Yang An, Wen Ting Zhang, Yi He

Let ${\mathcal{O}\mathcal{P}}_n$ be the monoid of all orientation-preserving full transformations on $X_n=\{1,\dots ,n\}$ with the natural order. For $\alpha \in {\mathcal{O}\mathcal{P}}_n$, let $F(α)=\{y\in X_…