Systems of Inequalities and Numerical Semigroups

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 N m −1 . Finally, this result is particularized to the symmetric case.