= Cyclic Turán covering construction
{title2=$\left((\ell-1)/r\right)^{\ell-1}$}
With $r$ balanced cyclically ordered vertex classes and $2\le\ell\le r+1$, include an $\ell$-set if some start has at least $k+1$ vertices in its first $k$ classes for every $1\le k\le\ell-1$. The <cycle lemma> implies every $(r+1)$-set contains an edge. Its asymptotic density is $((\ell-1)/r)^{\ell-1}$; taking the <hypergraph complement> gives a lower bound for the <Turán density> of a complete uniform hypergraph.
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