A numerical semigroup S is dense if for all \(s\in S\backslash \{0\}\) we have \(\left\{ s-1,s+1\right\} \cap S\ne \emptyset \). We give algorithms to compute the whole set of dense numerical semigroups with fixed genus, Frobenius number and multiplicity. Furthermore, we solve the Frobenius problem for dense numerical semigroups with embedding dimension three.

中文翻译：

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密集数值半群

如果对于所有\（s \ S \反斜杠\ {0 \} \），我们都有\（\ left \ {s-1，s + 1 \ right \} \ cap S \ ne \ emptyset，则数值半群S是密集的\）。我们给出算法来计算具有固定属，Frobenius数和多重性的整个密集数值半群。此外，我们解决了嵌入维数为3的稠密数值半群的Frobenius问题。