Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modular Frobenius pseudo-varieties   If $m \in \mathbb{N}$ and $A$ is a finite subset of $\bigcup_{k \in
\mathbb{N} \setminus \{0,1\}} \{1,\ldots,m-1\}^k$, then we denote by
\begin{align*} \mathscr{C}(m,A) = \left\{S\in \mathscr{S}_m \mid
s_1+\cdots+s_k-m \in S \mbox{ if } (s_1,\ldots,s_k)\in S^k \mbox{ and }\right.
\\ \left.(s_1 \bmod m, \ldots, s_k \bmod m)\in A \right\}. \end{align*} In this
work we prove that $\mathscr{C}(m,A)$ is a Frobenius pseudo-variety. We also
show algorithms that allows us to establish whether a numerical semigroup
belongs to $\mathscr{C}(m,A)$ and to compute all the elements of
$\mathscr{C}(m,A)$ with a fixed genus. Moreover, we introduce and study three
families of numerical semigroups, called of second-level, thin and strong, and
corresponding to $\mathscr{C}(m,A)$ when $A=\{1,\ldots,m-1\}^3$,
$A=\{(1,1),\ldots,(m-1,m-1)\}$, and $A=\{1,\ldots,m-1\}^2 \setminus
\{(1,1),\ldots,(m-1,m-1)\}$, respectively.

15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph