On permutation numerical semigroups

Simone Ugolini

On permutation numerical semigroups

Number Theory 2016-09-27 v2

Authors: Simone Ugolini

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.

Keywords

semigroup theory permutations permutation groups

Cite

@article{arxiv.1609.01133,
  title  = {On permutation numerical semigroups},
  author = {Simone Ugolini},
  journal= {arXiv preprint arXiv:1609.01133},
  year   = {2016}
}

Comments

45 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

On permutation numerical semigroups

Abstract

Keywords

Cite

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