Communications of the
Korean Mathematical Society CKMS

In this note, we aim to correct some of the results presented in \cite{Fernandes:2023}. Namely, the statements of Proposition 2.1, Corollary 2.2, Corollary 2.3, Theorem 2.4 and Theorem 2.6, concerning only the monoids $\mathcal{O}\mathcal{P}_n$ and $\mathcal{P}\mathcal{O}\mathcal{P}_n$, have to exclude transformations of rank two. All other results of \cite{Fernandes:2023}, as well as those mentioned above but for the monoids $\mathcal{O}\mathcal{R}_n$ and $\mathcal{P}\mathcal{O}\mathcal{R}_n$, do not require correction.

Keywords: Orientation-preserving transformations, orientation-reversing transformations, oriented transformations

MSC numbers: Primary 20M20

Supported by: This work is funded by national funds through the FCT - Funda\c c\~ao para a Ci\^encia~e~a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/\\UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications).