Symmetric numerical semigroups with arbitrary multiplicity and embedding dimension

Rosales, J.

doi:10.1090/S0002-9939-01-05819-1

Symmetric numerical semigroups with arbitrary multiplicity and embedding dimension
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by J. C. Rosales

Proc. Amer. Math. Soc. 129 (2001), 2197-2203

DOI: https://doi.org/10.1090/S0002-9939-01-05819-1

Published electronically: January 17, 2001

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Abstract:

We construct symmetric numerical semigroups $S$ for every minimal number of generators $\mu (S)$ and multiplicity $\mathsf {m}(S)$, $2\leq \mu (S)\leq \mathsf {m}(S)-1$. Furthermore we show that the set of their defining congruence is minimally generated by $\mu (S)(\mu (S)-1)/2-1$ elements.

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