Main Article Content
The complexity of a numerical semigroup
Abstract
Let S and Δ be numerical semigroups. A numerical semigroup S is an I(Δ)-semigroup if S \ {0} is an ideal of Δ. We denote by 
S is an I(Δ)-semigroup}, and we say that Δ is an ideal extension of S if S 
.
In this work, we present an algorithm to build all the ideal extensions of a numerical semigroup. We recursively denote by 
and 
for all k ∈ N. The complexity of a numerical semigroup S is the minimum of the set 
. In addition, we introduce an algorithm to compute all the numerical semigroups with fixed multiplicity and complexity.
