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Note on a theorem of Eliahou

Hellus, M. ; Rechenauer, A. ; Waldi, R.


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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