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Patterns of ideals of numerical semigroups

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Abstract

This article introduces patterns of ideals of numerical semigroups, thereby unifying previous definitions of patterns of numerical semigroups. Several results of general interest are proved. More precisely, this article presents results on the structure of the image of patterns of ideals, and also on the structure of the sets of patterns admitted by a given ideal.

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Acknowledgments

My gratitute goes to Ralf Fröberg and Christian Gottlieb without whom this article would not have been written, and for their extensive and invaluable help during its elaboration. I also want to thank Pedro García-Sánchez for a large number of very useful comments and for his help in the implementation for GAP. I also acknowledge partial support from the Spanish MEC project ICWT (TIN2012-32757) and ARES (CONSOLIDER INGENIO 2010 CSD2007-00004).

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Authors and Affiliations

  1. School of Engineering Science, University of Skövde, Box 408, 54128, Skövde, Sweden

    Klara Stokes

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  1. Klara Stokes
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Correspondence to Klara Stokes.

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Communicated by Fernando Torres.

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Stokes, K. Patterns of ideals of numerical semigroups. Semigroup Forum 93, 180–200 (2016). https://doi.org/10.1007/s00233-015-9741-1

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  • DOI: https://doi.org/10.1007/s00233-015-9741-1

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