Eliahou number, Wilf function and concentration of a numerical semigroup
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 a negative Eliahou number in terms of its multiplicity, concentration and Wilf function. Also, we show new...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | español |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/71833 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/71833 |
| Access Level: | acceso abierto |
| Palabra clave: | 512 512.53 Numerical semigroup Coin change problem Wilf conjecture Eliahou number Concentration. Álgebra Grupos (Matemáticas) 1201 Álgebra |
| Sumario: | 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 a negative Eliahou number in terms of its multiplicity, concentration and Wilf function. Also, we show new examples of numerical semigroups with a negative Eliahou number satisfying the Wilf conjecture. 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. These results provide new evidences in favour of the Wilf conjecture. |
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