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Turkish Journal of Mathematics

Abstract

A numerical semigroup is perfect if it does not have isolated gaps. In this paper we will order the perfect numerical semigroups with a fixed multiplicity. This ordering allows us to give an algorithm procedure to obtain them. We also study the perfect monoid, which is a subset of $\N$ that can be expressed as an intersection of perfect numerical semigroups, and we present the perfect monoid generated by a subset of $\N$. We give an algorithm to calculate it. We study the perfect closure of a numerical semigroup, as well as the perfect numerical semigroup with maximal embedding dimension, in particular Arf and saturated numerical semigroups.

DOI

10.3906/mat-1901-111

Keywords

Arf semigroup, embedding dimension, Frobenius number, genus, multiplicity, numerical semigroup, saturated semigroup

First Page

1742

Last Page

1754

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