Eliahou number, Wilf function and concentration of a numerical semigroup
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866909457218273280 |
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| author | Almirón, Patricio Moyano-Fernández, Julio José |
| author_facet | Almirón, Patricio Moyano-Fernández, Julio José |
| contents | We give an estimate of the minimal positive value of the Wilf function of a numerical semigroup in terms of its concentration. We describe necessary conditions for a numerical semigroup to have negative Eliahou number in terms of its multiplicity, concentration and Wilf function. Also, we show new examples of numerical semigroups with negative Eliahou number. In addition, we introduce the notion of highly dense numerical semigroup; this yields a new family of numerical semigroups satisfying the Wilf conjecture. Moreover, we use the Wilf function of a numerical semigroup to prove that the Eliahou number of a highly dense numerical semigroup is positive under certain additional hypothesis. In particular, these results provide new evidences in favour of the Wilf conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_03793 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Eliahou number, Wilf function and concentration of a numerical semigroup Almirón, Patricio Moyano-Fernández, Julio José Commutative Algebra Combinatorics Primary: 20M14, Secondary: 05A19 We give an estimate of the minimal positive value of the Wilf function of a numerical semigroup in terms of its concentration. We describe necessary conditions for a numerical semigroup to have negative Eliahou number in terms of its multiplicity, concentration and Wilf function. Also, we show new examples of numerical semigroups with negative Eliahou number. In addition, we introduce the notion of highly dense numerical semigroup; this yields a new family of numerical semigroups satisfying the Wilf conjecture. Moreover, we use the Wilf function of a numerical semigroup to prove that the Eliahou number of a highly dense numerical semigroup is positive under certain additional hypothesis. In particular, these results provide new evidences in favour of the Wilf conjecture. |
| title | Eliahou number, Wilf function and concentration of a numerical semigroup |
| topic | Commutative Algebra Combinatorics Primary: 20M14, Secondary: 05A19 |
| url | https://arxiv.org/abs/2104.03793 |