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Symmetric numerical semigroups with arbitrary multiplicity and embedding dimension
Authors:J C Rosales
Institution:Departamento de Álgebra, Universidad de Granada, E-18071 Granada, Spain
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.

Keywords:Symmetric numerical semigroup  multiplicity  embedding dimension
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