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{\bf Peter Keevash}
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{\bf The Tur\'an Problem for Hypergraphs of Fixed Size}
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We obtain a general bound on the Tur\'an density of
a hypergraph in terms of the number of edges that
it contains. If ${\cal F}$ is an $r$-uniform
hypergraph with $f$ edges we show that
$$\pi({\cal F}) < 
{f-2\over f-1} - \big(1+o(1)\big)(2r!^{2/r}f^{3-2/r})^{-1},$$
for fixed $r \geq 3$ and $f \rightarrow \infty$.

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