Arf good semigroups with fixed genus

Abstract

In this paper we give an algorithm for the computation of all the Arf numerical semigroups with a given genus. Moreover, we generalize the concept of genus of a numerical semigroup to good semigroups of ${\mathbb{N}}^r$ and we give a procedure to calculate all the Arf semigroups of ${\mathbb{N}}^r$ with a given genus.

18 pages. arXiv admin note: text overlap with arXiv:1802.00809