Wilf’s conjecture and Macaulay’s theorem
Shalom Eliahou
Université du Littoral Côte d’Opale, Calais, France
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Abstract
Let be a numerical semigroup with multiplicity , conductor and minimally generated by elements. Let be the set of elements of which are smaller than . Wilf conjectured in 1978 that is bounded below by . We show here that if , then satisfies Wilf's conjecture. Combined with a recent result of Zhai, this implies that the conjecture is asymptotically true as the genus goes to infinity. One main tool in this paper is a classical theorem of Macaulay on the growth of Hilbert functions of standard graded algebras.
Cite this article
Shalom Eliahou, Wilf’s conjecture and Macaulay’s theorem. J. Eur. Math. Soc. 20 (2018), no. 9, pp. 2105–2129
DOI 10.4171/JEMS/807