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Semigroup Forum

, Volume 97, Issue 1, pp 64–74 | Cite as

Note on a theorem of Eliahou

  • M. Hellus
  • A. Rechenauer
  • R. Waldi
Research Article
  • 79 Downloads

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.

References

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgGermany
  2. 2.RegensburgGermany

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