M. B. Branco

Systems of Inequalities and Numerical Semigroups

A one-to-one correspondence is described between the setS(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.

Irreducible numerical semigroups with arbitrary multiplicity and embedding dimension

We give families of irreducible numerical semigroups with even conductor and with arbitrary multiplicity and embedding dimension. We also study minimal presentations for these families of numerical semigroups.

Bracelet monoids and numerical semigroups

Given positive integers

The Number of Saturated Numerical Semigroups with a Determinate Genus

n_1,\ldots ,n_p

The Frobenius problem for Mersenne numerical semigroups

n1,…,np, we say that a submonoid M of

The Frobenius problem for numerical semigroups

({\mathbb N},+)