Abstract
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.
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The authors would also like to thank the referee for the constructive and helpful comments and corrections.
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Communicated by Benjamin Steinberg.
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The first author was partially supported by the research groups FQM-343 FQM-5849 (Junta de Andalucia/Feder) and by the project MTM2014-55367-P (MINECO/FEDER, UE). The second author is supported by the project FCT PTDC/MAT/73544/2006.
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Rosales, J.C., Branco, M.B. & Faria, M.C. Dense numerical semigroups. Semigroup Forum 103, 221–235 (2021). https://doi.org/10.1007/s00233-021-10190-1
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DOI: https://doi.org/10.1007/s00233-021-10190-1