On permutation numerical semigroups

Abstract

In this paper we introduce the notion of $n$-permutation numerical semigroup. While there are just three $2$-permutation numerical semigroups, there are infinitely many $n$-permutation numerical semigroups if $n>2$. We construct $16$ families of $3$-permutation numerical semigroups and one family of $n$-permutation numerical semigroups. Finally we present some experimental data, which seem to support a conjecture about the classification of $3$-permutation numerical semigroups.

arXiv comment45 pages. Introduction revised. Fixed some inaccuracies in the classification of 2-permutation semigroups. Some proofs in Section 3 have been revised and two families have been merged.. Section 4 has been revised including some experimental data