Elements with unique length factorization of a numerical semigroup generated by three consecutive numbers
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914746291191808 |
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| author | García-Sánchez, Pedro A. González, Laura Planas-Vilanova, Francesc |
| author_facet | García-Sánchez, Pedro A. González, Laura Planas-Vilanova, Francesc |
| contents | Let $S$ be the numerical semigroup generated by three consecutive numbers $a,a+1,a+2$, where $a\in\mathbb{N}$, $a\geq 3$. We describe the elements of $S$ whose factorizations have all the same length, as well as the set of factorizations of each of these elements. We give natural partitions of this subset of $S$ in terms of the length and the denumerant. By using Apéry sets and Betti elements we are able to extend some results, first obtained by elementary means. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06358 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Elements with unique length factorization of a numerical semigroup generated by three consecutive numbers García-Sánchez, Pedro A. González, Laura Planas-Vilanova, Francesc Combinatorics Commutative Algebra 20M14 Let $S$ be the numerical semigroup generated by three consecutive numbers $a,a+1,a+2$, where $a\in\mathbb{N}$, $a\geq 3$. We describe the elements of $S$ whose factorizations have all the same length, as well as the set of factorizations of each of these elements. We give natural partitions of this subset of $S$ in terms of the length and the denumerant. By using Apéry sets and Betti elements we are able to extend some results, first obtained by elementary means. |
| title | Elements with unique length factorization of a numerical semigroup generated by three consecutive numbers |
| topic | Combinatorics Commutative Algebra 20M14 |
| url | https://arxiv.org/abs/2404.06358 |