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arXiv · 2503.19459

On the monoid of partial order-preserving transformations of a finite chain whose domains and ranges are intervals

Hayrullah Ayık·Vítor H. Fernandes·Emrah Korkmaz
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Abstract

In this paper, we consider the monoid $\mathcal{PIO}_{n}$, of all partial order-preserving transformations on a chain with $n$ elements whose domains and ranges are intervals, along with its submonoid $\mathcal{PIO}_{n}^-$ of order-decreasing transformations. Our main aim is to give presentations for $\mathcal{PIO}_{n}^-$ and $\mathcal{PIO}_{n}$. Moreover, for both monoids, we describe regular elements and determine their ranks, cardinalities and the numbers of idempotents and nilpotents.

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Hayrullah Ayık, Vítor H. Fernandes, Emrah Korkmaz. 2025-03-25. On the monoid of partial order-preserving transformations of a finite chain whose domains and ranges are intervals. https://arxiv.org/abs/2503.19459

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