Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Asymptotic Growth of the Number of Tree-Child Networks   In a recent paper, McDiarmid, Semple, and Welsh (2015) showed that the number
of tree-child networks with $n$ leaves has the factor $n^{2n}$ in its main
asymptotic growth term. In this paper, we improve this by completely
identifying the main asymptotic growth term up to a constant. More precisely,
we show that the number of tree-child networks with $n$ leaves grows like \[
\Theta\left(n^{-2/3}e^{a_1(3n)^{1/3}}\left(\frac{12}{e^2}\right)^{n}n^{2n}\right),
\] where $a_1=-2.338107410\cdots$ is the largest root of the Airy function of
first kind. For the proof, we bijectively map the underlying graph-theoretical
problem onto a problem on words. For the latter, we can find a recurrence to
which a recent powerful asymptotic method of Elvey Price, Fang, and Wallner
(2019) can be applied.

9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int