Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An asymptotic result concerning a question of Wilf   Let $\Lambda$ be a numerical semigroup with embedding dimension $e(\Lambda)$.
Define $c(\Lambda)$ to be one plus the largest integer not in $\Lambda$, and
define $c'(\Lambda)$ to be the number of elements in $\Lambda$ less than
$c(\Lambda)$. It was asked by Wilf whether $\frac{c'(\Lambda)}{c(\Lambda)} \ge
\frac{1}{e(\Lambda)}$ always holds. We prove an asymptotic version of this
conjecture: we show that for a fixed positive integer $k$ and any $\epsilon >
0$, the inequality $\frac{c'(\Lambda)}{c(\Lambda)} \ge \frac{1}{k} - \epsilon$
holds for all but finitely many numerical semigroups $\Lambda$ satisfying
$e(\Lambda) = k$.

14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio