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V\'\i tor H. Fernandes,Teresa M. Quinteiro 대한수학회 2016 대한수학회보 Vol.53 No.2
In this note we consider the monoid $\PODI_n$ of all monotone partial permutations on $\{1,\ldots,n\}$ and its submonoids $\DP_n$, $\POI_n$ and $\ODP_n$ of all partial isometries, of all order-preserving partial permutations and of all order-preserving partial isometries, respectively. We prove that both the monoids $\POI_n$ and $\ODP_n$ are quotients of bilateral semidirect products of two of their remarkable submonoids, namely of extensive and of co-extensive transformations. Moreover, we show that $\PODI_n$ is a quotient of a semidirect product of $\POI_n$ and the group $\mathcal{C}_2$ of order two and, analogously, $\DP_n$ is a quotient of a semidirect product of $\ODP_n$ and $\mathcal{C}_2$.
Oriented transformations on a finite chain: another description
V\'\i tor H. Fernandes 대한수학회 2023 대한수학회논문집 Vol.38 No.3
Following the new description of an oriented full transformation on a finite chain given recently by Higgins and Vernitski in \cite{Higgins&Vernitski:2022}, in this short note we present a refinement of this description which is extendable to partial transformations and to injective partial transformations.