Numerical semigroups that can be expressed as an intersection of symmetric numerical semigroups (Q1612128)

A numerical semigroup \(S\) is an additive submonoid of \(\mathbb{Z}_+\) whose complement \(\mathbb{Z}_+-S\) is finite. The Frobenius number of \(S\), denoted by \(g(S)\), is the greatest integer not belonging to \(S\). A numerical semigroup \(S\) is called symmetric if \(g(S)-z\in S\) for each \(z\in\mathbb{Z}-S\). In this paper, the authors study numerical semigroups which are the intersection of a finite number of symmetric numerical semigroups and they give an algorithm to find this decomposition. They also investigate which numerical semigroups \(S\) are the intersection of a finite number of symmetric numerical semigroups all of which have the same Frobenius number or the same multiplicity as \(S\).