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Patterns on the Numerical Duplication by Their Admissibility Degree

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Numerical Semigroups

Part of the book series: Springer INdAM Series ((SINDAMS,volume 40))

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Abstract

We develop the theory of patterns on numerical semigroups in terms of the admissibility degree. We prove that the Arf pattern induces every strongly admissible pattern, and determine all patterns equivalent to the Arf pattern. We study patterns on the numerical duplication when d ≫ 0. We also provide a definition of patterns on rings.

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Acknowledgements

I would like to thank Marco D’Anna for his constant support, Maria Bras-Amóros for useful conversations and email exchanges, and Nicola Maugeri for indicating some good references.

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Authors and Affiliations

  1. University of Catania, Catania, Italy

    Alessio Borzì

  2. Scuola Superiore di Catania, Catania, Italy

    Alessio Borzì

Authors
  1. Alessio Borzì
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Correspondence to Alessio Borzì .

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Editors and Affiliations

  1. Matematica, Sapienza University of Rome, Roma, Italy

    Valentina Barucci

  2. Department of Mathematics & Statistics, Sam Houston State University, Huntsville, TX, USA

    Scott Chapman

  3. Dip di Matematica e Informatica, Università di Catania, Catania, Catania, Italy

    Marco D'Anna

  4. Mathematics, Stockhom University, Stockholm, Sweden

    Ralf Fröberg

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Borzì, A. (2020). Patterns on the Numerical Duplication by Their Admissibility Degree. In: Barucci, V., Chapman, S., D'Anna, M., Fröberg, R. (eds) Numerical Semigroups . Springer INdAM Series, vol 40. Springer, Cham. https://doi.org/10.1007/978-3-030-40822-0_2

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