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Almost-Positioned Numerical Semigroups

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Abstract

A numerical semigroup S is almost-positioned if for all \(s\in {{\mathbb {N}}}\backslash S\) we have that \(\mathrm{F}(S)+\mathrm{{m}}(S)+1-s\in S\). In this note we give algorithmics for computing the whole set of almost-positioned numerical semigroup with fixed multiplicity and Frobenius number. Moreover, we prove Wilf’s conjecture for this type of numerical semigroups.

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Acknowledgements

The authors would also like to thank the referee for the constructive and helpful comments and corrections

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Authors and Affiliations

  1. Departamento de Matemática, Universidade de Évora, 7000, Évora, Portugal

    M. B. Branco

  2. Área Departamental de Física, Instituto Sup. Eng. de Lisboa, 1959-007, Lisboa, Portugal

    M. C. Faria

  3. Departamento de Álgebra, Universidad de Granada, 18071, Granada, Spain

    J. C. Rosales

Authors
  1. M. B. Branco
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  2. M. C. Faria
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  3. J. C. Rosales
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Correspondence to M. B. Branco.

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The first author is supported by the project FCT PTDC/MAT/73544/2006. The third autor was partially supported by the research groups FQM-343 (Junta de Andalucia/Feder) and by the Project MTM2017-84890-P.

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Branco, M.B., Faria, M.C. & Rosales, J.C. Almost-Positioned Numerical Semigroups. Results Math 76, 63 (2021). https://doi.org/10.1007/s00025-021-01372-y

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  • DOI: https://doi.org/10.1007/s00025-021-01372-y

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