On oriented alternating inverse monoids
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917942870933504 |
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| author | Fernandes, Vítor Hugo |
| author_facet | Fernandes, Vítor Hugo |
| contents | In this paper, we consider the inverse submonoids $AOR_n$ of oriented transformations and $AOP_n$ of orientation-preserving transformations of the alternating inverse monoid $AI_n$ on a chain with $n$ elements. We compute the cardinalities, describe the Green's structures and the congruences, and calculate the ranks of $AOR_n$ and $AOP_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00832 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On oriented alternating inverse monoids Fernandes, Vítor Hugo Rings and Algebras 20M20, 20M18, 20M10 In this paper, we consider the inverse submonoids $AOR_n$ of oriented transformations and $AOP_n$ of orientation-preserving transformations of the alternating inverse monoid $AI_n$ on a chain with $n$ elements. We compute the cardinalities, describe the Green's structures and the congruences, and calculate the ranks of $AOR_n$ and $AOP_n$. |
| title | On oriented alternating inverse monoids |
| topic | Rings and Algebras 20M20, 20M18, 20M10 |
| url | https://arxiv.org/abs/2503.00832 |