Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The complexity of a numerical semigroup   Let $S$ and $\Delta$ be numerical semigroups. A numerical semigroup $S$ is an
$\mathbf{I}(\Delta)$-{\it semigroup} if $S\backslash \{0\}$ is an ideal of
$\Delta$. We will denote by $\mathcal{J}(\Delta)=\{S \mid S \text{ is an
$\mathbf{I}(\Delta)$-semigroup} \}.$ We will say that $\Delta$ is {\it an ideal
extension of } $S$ if $S\in \mathcal{J}(\Delta).$ In this work, we present an
algorithm that allows to build all the ideal extensions of a numerical
semigroup. We can recursively denote by $\mathcal{J}^0(\mathbb{N})=\mathbb{N},$
$\mathcal{J}^1(\mathbb{N})=\mathcal{J}(\mathbb{N})$ and
$\mathcal{J}^{k+1}(\mathbb{N})=\mathcal{J}(\mathcal{J}^{k}(\mathbb{N}))$ for
all $k\in \mathbb{N}.$ The complexity of a numerical semigroup $S$ is the
minimun of the set $\{k\in \mathbb{N}\mid S \in \mathcal{J}^k(\mathbb{N})\}.$
In addition, we will give an algorithm that allows us to compute all the
numerical semigroups with fixed multiplicity and complexity.

30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org