Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved bounds on the extremal function of hypergraphs   A fundamental problem in pattern avoidance is describing the asymptotic
behavior of the extremal function and its generalizations. We prove an
equivalence between the asymptotics of the graph extremal function for a class
of bipartite graphs and the asymptotics of the matrix extremal function. We use
the equivalence to prove several new bounds on the extremal functions of
graphs. We develop a new method to bound the extremal function of hypergraphs
in terms of the extremal function of their associated multidimensional
matrices, improving the bound of the extremal function of $d$-permutation
hypergraphs of length $k$ from $O(n^{d-1})$ to $2^{O(k)}n^{d-1}$.

29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio