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 set L of integers greater than or equal to 2 there are a numerical monoid H and a squarefree element a ∈ H whose set of lengths L(a) is equal to L.

Mots clés: numerical monoids; numerical semigroup algebras; sets of lengths; sets of distances

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

Alfred Geroldinger, Wolfgang Schmid. A realization theorem for sets of lengths in numerical monoids. Forum Mathematicum, 2018, 30 (5), pp.1111-1118. ⟨10.1515/forum-2017-0180⟩. ⟨hal-01615120v2⟩