Perfect numerical semigroups
Authors : María Ángeles Moreno Frías, Jose Carlos Rosales
Pages : 1742-1754
View : 8 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : Arf semigroup, embedding dimension, Frobenius number, genus, multiplicity, numerical semigroup, saturated semigroup