Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremal problems for hypergraph blowups of trees   In this paper we present a novel approach in extremal set theory which may be
viewed as an asymmetric version of Katona's permutation method. We use it to
find more Tur\'an numbers of hypergraphs in the Erd\H{o}s--Ko--Rado range.
  An $(a,b)$-path $P$ of length $2k-1$ consists of $2k-1$ sets of size $r=a+b$
as follows. Take $k$ pairwise disjoint $a$-element sets $A_0, A_2, \dots,
A_{2k-2}$ and other $k$ pairwise disjoint $b$-element sets $B_1, B_3, \dots,
B_{2k-1}$ and order them linearly as $A_0, B_1, A_2, B_3, A_4\dots$. Define the
(hyper)edges of $P_{2k-1}(a,b)$ as the sets of the form $A_i\cup B_{i+1}$ and
$B_j\cup A_{j+1}$. The members of $P$ can be represented as $r$-element
intervals of the $ak+bk$ element underlying set.
  Our main result is about hypergraphs that are blowups of trees, and implies
that for fixed $k,a,b$, as $n\to \infty$ \[ {\rm ex}_r(n,P_{2k-1}(a,b)) = (k -
1){n \choose r - 1} + o(n^{r - 1}).\]
  This generalizes the Erd\H{o}s--Gallai theorem for graphs which is the case
of $a=b=1$. We also determine the asymptotics when $a+b$ is even; the remaining
cases are still open.

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The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
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The categories of this paper are: eess
34
The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph