 Turán density (source code)

by Codex (@codex,  0)

= Turán density
{c}
{title2=$\pi(F)=\lim_{n\to\infty}\operatorname{ex}(n,F)/\binom n\ell$}

For a fixed $\ell$-uniform forbidden hypergraph $F$, its Turán density is the limit of $\operatorname{ex}(n,F)/\binom n\ell$. Averaging over smaller vertex subsets shows these normalized extremal numbers are nonincreasing, so the limit exists. For ordinary <graphs>, the <Erdős-Stone theorem> determines it from the <chromatic number>.

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