Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trees with minimum number of infima closed sets   Let $T$ be a rooted tree, and $V(T)$ its set of vertices. A subset $X$ of
$V(T)$ is called an infima closed set of $T$ if for any two vertices $u,v\in
X$, the first common ancestor of $u$ and $v$ is also in $X$. This paper
determines the trees with minimum number of infima closed sets among all rooted
trees of given order, thereby answering a question of Klazar. It is shown that
these trees are essentially complete binary trees, with the exception of
vertices at the last levels. Moreover, an asymptotic estimate for the minimum
number of infima closed sets in a tree with $n$ vertices is also provided.

35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas