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Constructing the set of complete intersection numerical semigroups with a given Frobenius number

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Abstract

Delorme suggested that the set of all complete intersection numerical semigroups can be computed recursively. We have implemented this algorithm, and particularized it to several subfamilies of this class of numerical semigroups: free and telescopic numerical semigroups, and numerical semigroups associated to an irreducible plane curve singularity. The recursive nature of this procedure allows us to give bounds for the embedding dimension and for the minimal generators of a semigroup in any of these families.

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Authors and Affiliations

  1. Département de Mathématiques, LAREMA, UMR 6093, Université d’Angers, 2 bd Lavoisier, 49045 , Angers Cedex 01, France

    A. Assi

  2. Departamento de Álgebra, Universidad de Granada, 18071 , Granada, Spain

    P. A. García-Sánchez

Authors
  1. A. Assi
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  2. P. A. García-Sánchez
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Correspondence to A. Assi.

Additional information

The first author is partially supported by the project GDR CNRS 2945.

The second author is supported by the projects MTM2010-15595, FQM-343, FQM-5849, and FEDER funds. This research was performed while the second author visited the Université d’Angers as invited lecturer, and he wants to thank the Département de Mathématiques of this university for its kind hospitality. The authors would like to thank the referees for their suggestions, comments and examples provided.

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Assi, A., García-Sánchez, P.A. Constructing the set of complete intersection numerical semigroups with a given Frobenius number. AAECC 24, 133–148 (2013). https://doi.org/10.1007/s00200-013-0186-z

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  • DOI: https://doi.org/10.1007/s00200-013-0186-z

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