@article {16626,
	title = {On semigroups of orientation-preserving partial permutations with restricted range},
	year = {Submitted},
	abstract = {<p>Let $\Omega_n$ be a finite chain with $n$ elements $(n\in\mathbb{N})$, and let $\mathcal{POPI}_{n}$ be the semigroup of all injective orientation-preserving partial transformations of $\Omega_n$. In this paper, for any nonempty subset $Y$ of $\Omega_n$, we consider the subsemigroup $\mathcal{POPI}_{n}(Y)$ of $\mathcal{POPI}_{n}$ of all transformations with range contained in $Y$. We describe the Green{\textquoteright}s relations and study the regularity of $\mathcal{POPI}_{n}(Y)$. Moreover, we calculate the rank of $\mathcal{POPI}_{n}(Y)$ and determine when two semigroups of this type are isomorphic.</p>
},
	url = {https://doi.org/10.48550/arXiv.2401.02185},
	author = {De Biao Li and Fernandes, V{\'\i}tor H.}
}
