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The numerical duplication of a numerical semigroup

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Abstract

In this paper we present and study the numerical duplication of a numerical semigroup, a construction that, starting with a numerical semigroup S and a semigroup ideal E⊆S, produces a new numerical semigroup, denoted by S⋈b E (where b is any odd integer belonging to S), such that S=(S⋈b E)/2. In particular, we characterize the ideals E such that S⋈b E is almost symmetric and we determine its type.

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Acknowledgements

The authors thank Fernando Torres for pointing out the connection between numerical duplication and Weierstrass semigroup theory.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Viale A. Doria 6, 95125, Catania, Italy

    M. D’Anna & F. Strazzanti

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  1. M. D’Anna
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  2. F. Strazzanti
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Correspondence to M. D’Anna.

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Communicated by Fernando Torres.

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D’Anna, M., Strazzanti, F. The numerical duplication of a numerical semigroup. Semigroup Forum 87, 149–160 (2013). https://doi.org/10.1007/s00233-012-9451-x

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  • DOI: https://doi.org/10.1007/s00233-012-9451-x

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