Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper Bounds For Families Without Weak Delta-Systems   For $k\geq3$, a collection of $k$ sets is said to form a \emph{weak
$\Delta$-system} if the intersection of any two sets from the collection has
the same size. Erd\H{o}s and Szemer\'{e}di asked about the size of the largest
family $\mathcal{F}$ of subsets of $\{1,\dots,n\}$ that does not contain a weak
$\Delta$-system. In this note we improve upon the best upper bound from
arXiv:1606.09575 and show that \[
|\mathcal{F}|\leq\left(\frac{2}{3}\Theta(C)+o(1)\right)^{n} \] where
$\Theta(C)$ is the capset capacity. In particular, this shows that \[
|\mathcal{F}|\leq(1.8367\dots+o(1))^{n}. \]

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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph