@article {5763,
	title = {On semigroups of orientation-preserving transformations with restricted range},
	journal = {Communications in Algebra (DOI:10.1080/00927872.2014.975345)},
	volume = {44},
	year = {2016},
	pages = {253-264},
	abstract = {<p>Let $X_n$ be a chain with n elements ($n\in\N$) and let $\OP_n$ be the monoid of all orientation-preserving transformations of $X_n$.  In this paper, for any nonempty subset $Y$ of $X_n$, we consider the subsemigroup $\OP_n(Y)$ of $\OP_n$ of all transformations with range contained in $Y$: we describe the largest regular subsemigroup of $\OP_n(Y)$, which actually coincides with its subset of all regular elements, and Green{\textquoteright}s relations on $\OP_n(Y)$. Also, we determine when two semigroups of the type $\OP_n(Y)$ are isomorphic and calculate their ranks. Moreover, a parallel study is presented for the correspondent subsemigroups of the monoid $\OR_n$ of all either orientation-preserving or orientation-reversing transformations of $X_n$. </p>
},
	url = {http://www.tandfonline.com/doi/pdf/10.1080/00927872.2014.975345},
	attachments = {https://docentes.fct.unl.pt/sites/default/files/vhf/files/opnyv2.pdf},
	author = {Fernandes, V{\'\i}tor H. and Preeyanuch Honyam and Quinteiro, Teresa M. and Boorapa Singha}
}
