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Gapsets and numerical semigroups


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.
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hal-01933259 , version 1 (23-11-2018)



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