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arXiv · 2401.02185

On semigroups of orientation-preserving partial permutations with restricted range

De Biao Li·Vítor H. Fernandes
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Abstract

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'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.

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De Biao Li, Vítor H. Fernandes. 2024-01-04. On semigroups of orientation-preserving partial permutations with restricted range. https://arxiv.org/abs/2401.02185

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