Affine semigroups without consecutive small elements
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908414979866624 |
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| author | Rosales, J. C. Tapia-Ramos, R. Vigneron-Tenorio, A. |
| author_facet | Rosales, J. C. Tapia-Ramos, R. Vigneron-Tenorio, A. |
| contents | An $\mathcal{A}$-semigroup is a numerical semigroup without consecutive small elements. This work generalizes this concept to finite-complement submonoids of an affine cone $\mathcal{C}$. We develop algorithmic procedures to compute all $\mathcal{A}$-semigroups with a given Frobenius element (denoted by $\mathcal{A}(f)$), and with fixed Frobenius element and multiplicity. Moreover, we analyze the $\mathcal{A}(f)$-systems of generators. Furthermore, we study $\mathcal{A}$-numerical semigroups with maximal embedding dimension, fixed Frobenius number and multiplicity, providing an algorithm for their computation and a graphical classification. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_17152 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Affine semigroups without consecutive small elements Rosales, J. C. Tapia-Ramos, R. Vigneron-Tenorio, A. Commutative Algebra Combinatorics An $\mathcal{A}$-semigroup is a numerical semigroup without consecutive small elements. This work generalizes this concept to finite-complement submonoids of an affine cone $\mathcal{C}$. We develop algorithmic procedures to compute all $\mathcal{A}$-semigroups with a given Frobenius element (denoted by $\mathcal{A}(f)$), and with fixed Frobenius element and multiplicity. Moreover, we analyze the $\mathcal{A}(f)$-systems of generators. Furthermore, we study $\mathcal{A}$-numerical semigroups with maximal embedding dimension, fixed Frobenius number and multiplicity, providing an algorithm for their computation and a graphical classification. |
| title | Affine semigroups without consecutive small elements |
| topic | Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2506.17152 |