Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complexes of nearly maximum diameter   The diameter of a strongly connected $d$-dimensional simplicial complex is
the diameter of its dual graph. We provide a probabilistic proof of the
existence of $d$-dimensional simplicial complexes with diameter $ (\frac{1}{d
\cdot d!} - (\log n)^{-\epsilon}) n^d$. Up to the first order term, this is the
best possible lower bound for the maximum diameter of a $d$-complex on $n$
vertices as a simple volume argument shows that the diameter of a
$d$-dimensional simplicial complex is at most $ \frac{1}{d} \binom{n}{d}$. We
also find the right first-order asymptotics for the maximum diameter of a
$d$-pseudomanifold on $n$ vertices.

9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th