Abstract
A one‐to‐one correspondence is described between the set S(m) of numerical semigroups with multiplicity m and the set of non‐negative integer solutions of a system of linear Diophantine inequalities. This correspondence infers in S(m) a semigroup structure and the resulting semigroup is isomorphic to a subsemigroup of Nm−1. Finally, this result is particularized to the symmetric case.
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