Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decomposition of Triply Rooted Trees   In this paper, we give a decomposition of triply rooted trees into three
doubly rooted trees. This leads to a combinatorial interpretation of an
identity conjectured by Lacasse in the study of the PAC-Bayesian machine
learning theory, and proved by Younsi by using the Hurwitz identity on
multivariate Abel polynomials. We also give a bijection between the set of
functions from $[n+1]$ to $[n]$ and the set of triply rooted trees on $[n]$,
which leads to the refined enumeration of functions from $[n+1]$ to $[n]$ with
respect to the number of elements in the orbit of $n+1$ and the number of
periodic points.

16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys