A graph of all numerical semigroups


A numerical semigroup is a co-finite submonid of the monoid of the non-negative integers, under addition. Despite being very simple structures, numerical semigroups are fascinating objects. On the one hand, they appear in many areas of mathematics; on the other hand, one finds problems that are far from simple in its study. In this seminar we will consider a directed graph whose nodes are numerical semigroups. Edges starting in a numerical semigroup end in another one which is obtained from the first by removing one element. A generating tree for that graph will be constructed. Throughout the construction, as long as the terminology is introduced, we will talk about some problems for which solutions are known and we will also talk about some open problems or conjectures.