When the catenary degree meets the tame degree in embedding dimension 3 numerical semigroups

A numerical semigroup is a subset of N, containing the zero, and closed under addition. A numerical semigroup is finitely generated, the number of any minimal set of generators is called embedding dimension. The  factorization of an element in a numerical semigroup is not unique. Catenary and tame degree are two of the arithmetical invariants related to the factorizations in a numerical semigroup.  I characterize embedding dimension three numerical semigroups having the same catenary and tame degree.

I got my master degree in Universitá degli Studi di Catania, in Italy, I study for my thesis in Granada with professor García-Sanchez. I was hosted as a intern at Max-Plank Institute for Mathematics in Bonn in September.