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On the number of numerical semigroups containing two coprime integers \(p\) and \(q\)

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Abstract

We show that the number of numerical semigroups containing two given coprime numbers \(p\) and \(q\) agrees with a quasipolynomial in \(q\) of degree exactly \(p-1\) and having constant leading coefficient lying between \(\frac{1}{(p-1)!\cdot p!}\) and \(\frac{1}{(p-1)\cdot p!}\).

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Acknowledgments

We thank Helmut Knebl for leaving us his results.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Regensburg, 93040, Regensburg, Germany

    M. Hellus & R. Waldi

Authors
  1. M. Hellus
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  2. R. Waldi
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Correspondence to M. Hellus.

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Communicated by Fernando Torres.

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Hellus, M., Waldi, R. On the number of numerical semigroups containing two coprime integers \(p\) and \(q\) . Semigroup Forum 90, 833–842 (2015). https://doi.org/10.1007/s00233-015-9710-8

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  • DOI: https://doi.org/10.1007/s00233-015-9710-8

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