The tree of good semigroups in ${\mathbb{N}}^2$ and a generalization of the Wilf conjecture

Abstract

In this work, we study good semigroups of ${\mathbb{N}}^n$ introducing the definition of length and genus for these objects. We show how to count the local good semigroup with a fixed genus. Furthermore, we study the relationships of these concepts with other ones previously defined in the case of good semigroups with two branches.

30 pages, 4 figures, 1 table