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The set of numerical semigroups of a given genus

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Abstract

In this paper we present a new approach to construct the set of numerical semigroups with a fixed genus. Our methodology is based on the construction of the set of numerical semigroups with fixed Frobenius number and genus. An equivalence relation is given over this set and a tree structure is defined for each equivalence class. We also provide a more efficient algorithm based on the translation of a numerical semigroup to its so-called Kunz-coordinates vector.

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Acknowledgements

The authors were partially supported by the research group FQM-343 and the project FQM-5849 (Junta de Andalucía\FEDER). The first author was partially supported by the Juan de la Cierva grant JCI-2009-03896 and project MTM2010-19576-C02-01 (MICINN, Spain). The second author was partially supported by MTM2010-15595 (MICINN, Spain).

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Authors and Affiliations

  1. Dep. of Quantitative Methods for Economics & Business, Universidad de Granada, 18011, Granada, Spain

    V. Blanco

  2. Dep. of Algebra, Universidad de Granada, 18071, Granada, Spain

    J. C. Rosales

Authors
  1. V. Blanco
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  2. J. C. Rosales
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Correspondence to V. Blanco.

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Communicated by Benjamin Steinberg.

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Blanco, V., Rosales, J.C. The set of numerical semigroups of a given genus. Semigroup Forum 85, 255–267 (2012). https://doi.org/10.1007/s00233-012-9378-2

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