Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Further results on the inducibility of $d$-ary trees   A subset of leaves of a rooted tree induces a new tree in a natural way. The
density of a tree $D$ inside a larger tree $T$ is the proportion of such
leaf-induced subtrees in $T$ that are isomorphic to $D$ among all those with
the same number of leaves as $D$. The inducibility of $D$ measures how large
this density can be as the size of $T$ tends to infinity. In this paper, we
explicitly determine the inducibility in some previously unknown cases and find
general upper and lower bounds, in particular in the case where $D$ is
balanced, i.e., when its branches have at least almost the same size. Moreover,
we prove a result on the speed of convergence of the maximum density of $D$ in
strictly $d$-ary trees $T$ (trees where every internal vertex has precisely $d$
children) of a given size $n$ to the inducibility as $n \to \infty$, which
supports an open conjecture.

23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat