A realization theorem for sets of lengths in numerical monoids

Alfred Geroldinger (1) , Wolfgang Schmid (2)

1 IM - Institut für Mathematik [Graz]
2 LAGA - Laboratoire Analyse, Géométrie et Applications

We show that for every finite nonempty subset of N ≥2 there are a numerical monoid H and a squarefree element a ∈ H whose set of lengths L(a) is equal to L.

Domaines: Algèbre commutative [math.AC]; Théorie des nombres [math.NT]

Alfred Geroldinger, Wolfgang Schmid. A realization theorem for sets of lengths in numerical monoids. 2017. ⟨hal-01615120v1⟩