Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Density of Numerical sets associated to a Numerical semigroup   A numerical set is a co-finite subset of the natural numbers that contains
zero. Its Frobenius number is the largest number in its complement. Each
numerical set has an associated semigroup $A(T)=\{t\mid t+T\subseteq T\}$,
which has the same Frobenius number as $T$. For a fixed Frobenius number $f$
there are $2^{f-1}$ numerical sets. It is known that there is a number $\gamma$
close to $0.484$ such that the ratio of these numerical sets that are mapped to
$N_f=\{0\}\cup(f,\infty)$ is asymptotically $\gamma$. We identify a collection
of families $N(D,f)$ of numerical semigroups such that for a fixed $D$ the
ratio of the $2^{f-1}$ numerical sets that are mapped to $N(D,f)$ converges to
a positive limit as $f$ goes to infinity. We denote the limit as $\gamma_D$,
these constants sum up to $1$ meaning that they asymptotically account for
almost all numerical sets.

4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph