2022/02/02 by García-García, J. I., Moreno-Frías, M. A., Rosales, J. C. +1 · 1 citation
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2202.00920
Let S and Δ be numerical semigroups. A numerical semigroup S is an I(Δ)-\it semigroup if S\backslash \0\ is an ideal of Δ. We will denote by J(Δ)=\S | S is an I(Δ)-semigroup \. We will say that Δ is \it an ideal extension of S if S∈ J(Δ). In this work, we present an algorithm that allows to build all the ideal extensions of a numerical semigroup. We can recursively denote by J0(ℕ)=ℕ, J1(ℕ)=J(ℕ) and Jk+1(ℕ)=J(Jk(ℕ)) for all k∈ ℕ. The complexity of a numerical semigroup S is the minimun of the set \k∈ ℕ| S ∈ Jk(ℕ)\. In addition, we will give an algorithm that allows us to compute all the numerical semigroups with fixed multiplicity and complexity.