Numerical semigroups and affine spaces

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In this paper we show that every symmetric numerical semigroup H generated by three elements is of affine space type where a numerical semigroup is said to be of affine space type if a minimal embedding of its monomial curve into the affine space is derived from an embedding of some affine space into an affine space by substituting monomials. In the case of a symmetric numerical semigroup generated by four elements

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