Gapsets and numerical semigroups

Shalom Eliahou (1) , Jean Fromentin (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

For g ≥ 0, let n g denote the number of numerical semi-groups of genus g. A conjecture by Maria Bras-Amorós in 2008 states that the inequality n g ≥ n g−1 + n g−2 should hold for all g ≥ 2. Here we show that such an inequality holds for the very large subtree of numerical semigroups satisfying c ≤ 3m, where c and m are the conductor and multiplicity, respectively. Our proof is given in the more flexible setting of gapsets, i.e. complements in N of numerical semigroups.

Domaines: Combinatoire [math.CO]; Théorie des groupes [math.GR]

Shalom Eliahou, Jean Fromentin. Gapsets and numerical semigroups. 2018. ⟨hal-01933259⟩