On some affine semigroups characterized by a finite-state automata
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914095194701824 |
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| author | Farrán, J. I. Rosales, J. C. Tapia-Ramos, R. Vigneron-Tenorio, A. |
| author_facet | Farrán, J. I. Rosales, J. C. Tapia-Ramos, R. Vigneron-Tenorio, A. |
| contents | This work introduces a new kind of affine semigroups called $P$-semigroups. Within the framework of $\mathcal C$-semigroups, we define a finite-state automaton associated to them. Moreover, this automaton determines whether a $\mathcal C$-semigroup is a $P$-semigroup, which represents a bridge between affine semigroups and Discrete Mathematics. Furthermore, some algorithms for computing all the $P$-semigroups with a fixed Frobenius element, genus, or multiplicity are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13612 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On some affine semigroups characterized by a finite-state automata Farrán, J. I. Rosales, J. C. Tapia-Ramos, R. Vigneron-Tenorio, A. Commutative Algebra Combinatorics 20M14, 20M35, 05C05 This work introduces a new kind of affine semigroups called $P$-semigroups. Within the framework of $\mathcal C$-semigroups, we define a finite-state automaton associated to them. Moreover, this automaton determines whether a $\mathcal C$-semigroup is a $P$-semigroup, which represents a bridge between affine semigroups and Discrete Mathematics. Furthermore, some algorithms for computing all the $P$-semigroups with a fixed Frobenius element, genus, or multiplicity are provided. |
| title | On some affine semigroups characterized by a finite-state automata |
| topic | Commutative Algebra Combinatorics 20M14, 20M35, 05C05 |
| url | https://arxiv.org/abs/2510.13612 |