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


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.


  1. 1.
    Eliahou, S.: Wilf’s conjecture and Macaulay’s theorem, arXiv:1703.01761v1 (2017) [math.CO]
  2. 2.
    Fröberg, R., Gottlieb, C., Häggkvist, R.: On numerical semigroups, Semigroup Forum, Vol. 35(1):63–83 (1986/1987)Google Scholar
  3. 3.
    Knebl, H.: Berechnung gewisser Invarianten monomialer Kurven. Diplomarbeit University Regensburg (1979)Google Scholar
  4. 4.
    Stanley, R.P.: Enumerative Combinatorics, Vol. 1, Cambridge Studies in Adv. Math. Vol. 49. Cambridge University Press, Cambridge (1997)CrossRefGoogle Scholar
  5. 5.
    Wilf, H.S.: A circle-of-lights algorithm for the money-changing problem. Am. Math. Mon. 85, 562–565 (1978)MathSciNetMATHGoogle Scholar
  6. 6.
    Zhai, A.: An asymptotic result concerning a question of Wilf, arXiv:1111.2779v1 [math.CO]

Copyright information

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

Authors and Affiliations

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

Personalised recommendations