Arithmetic Varieties of Numerical semigroups.

Abstract

In this article we present the notion of arithmetic variety for numerical semigroups. We study various aspects related to these varieties such as the smallest arithmetic that contains a set of numerical semigroups and we exhibit the root three associated with an arithmetic variety. This tree is not locally finite; However, if the Frobenius number is fixed, the tree has many nodes and algorithms can be developed. All algorithms provided in this article include its (non-debugged) implementation in GAP.