On the monoid of partial order-preserving transformations of a finite chain whose domains and ranges are intervals
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910892486033408 |
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| author | Ayık, Hayrullah Fernandes, Vítor H. Korkmaz, Emrah |
| author_facet | Ayık, Hayrullah Fernandes, Vítor H. Korkmaz, Emrah |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19459 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the monoid of partial order-preserving transformations of a finite chain whose domains and ranges are intervals Ayık, Hayrullah Fernandes, Vítor H. Korkmaz, Emrah Rings and Algebras 20M20, 20M05, 20M10 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. |
| title | On the monoid of partial order-preserving transformations of a finite chain whose domains and ranges are intervals |
| topic | Rings and Algebras 20M20, 20M05, 20M10 |
| url | https://arxiv.org/abs/2503.19459 |