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Almost symmetric numerical semigroups

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Abstract

We study almost symmetric numerical semigroups and semigroup rings. We describe a characteristic property of the minimal free resolution of the semigroup ring of an almost symmetric numerical semigroup. For almost symmetric semigroups generated by four elements we will give a structure theorem by using the “row-factorization matrices”, introduced by Moscariello. As a result, we give a simpler proof of Komeda’s structure theorem of pseudo-symmetric numerical semigroups generated by four elements. Row-factorization matrices are also used to study shifted families of numerical semigroups.

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Duisburg-Essen, Campus Essen, 45117, Essen, Germany

    Jürgen Herzog

  2. Department of Mathematics, College of Humanities and Sciences, Nihon University, Setagaya-ku, Tokyo, 156-8550, Japan

    Kei-ichi Watanabe

Authors
  1. Jürgen Herzog
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  2. Kei-ichi Watanabe
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Correspondence to Jürgen Herzog.

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Communicated by Fernando Torres.

Dedicated to Professor Ernst Kunz.

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Herzog, J., Watanabe, Ki. Almost symmetric numerical semigroups. Semigroup Forum 98, 589–630 (2019). https://doi.org/10.1007/s00233-019-10007-2

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  • DOI: https://doi.org/10.1007/s00233-019-10007-2

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