Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A refined enumeration of $p$-ary labeled trees   Let $\mathcal{T}^{(p)}_n$ be the set of $p$-ary labeled trees on
$\{1,2,\dots,n\}$. A maximal decreasing subtree of an $p$-ary labeled tree is
defined by the maximal $p$-ary subtree from the root with all edges being
decreasing. In this paper, we study a new refinement $\mathcal{T}^{(p)}_{n,k}$
of $\mathcal{T}^{(p)}_n$, which is the set of $p$-ary labeled trees whose
maximal decreasing subtree has $k$ vertices.

33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat