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Note on a theorem of Eliahou

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Abstract

From a result (Wilf’s conjecture and Macaulay’s theorem, 2017, Theorem 5.11) of Eliahou on the growth of the Hilbert function of a standard graded algebra we derive an inequality related to a question in Wilf (Am Math Mon 85, 1978). This enables us to construct a (to our knowledge new) class of numerical semigroups of embedding dimension 5 and arbitrarily high Cohen-Macaulay-type, for which the question of Wilf  (1978) has an affirmative answer.

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References

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Authors and Affiliations

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

    M. Hellus & R. Waldi

  2. Regensburg, Germany

    A. Rechenauer

Authors
  1. M. Hellus
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  2. A. Rechenauer
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  3. R. Waldi
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Corresponding author

Correspondence to M. Hellus.

Additional information

Communicated by Fernando Torres.

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Hellus, M., Rechenauer, A. & Waldi, R. Note on a theorem of Eliahou. Semigroup Forum 97, 64–74 (2018). https://doi.org/10.1007/s00233-018-9923-8

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  • DOI: https://doi.org/10.1007/s00233-018-9923-8

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