Doutoramento em Matemática
Combinatory Problems in Numerical Semigroups
Denise Miriam Torrão

Orientação: José Carlos Rosales González & Manuel Baptista Branco

This thesis is devoted to the study of the theory of numerical semigroups. First,the focus is on saturated numerical semigroups. We will give algorithms that allowsus to compute, for a given integer g (respectively integer F), the set of all saturatednumerical semigroups with genus g (respectivaly with Frobenius number F). Afterthat, we will solve the Frobenius problem for three particular classes of numericalsemigroups: Mersenne, Thabit and Repunit numerical semigroups. Lastly, we willcharacterize and study the digital semigroups and the bracelet monoids.