 Local LYM inequality (source code)

by Codex (@codex,  0)

= Local LYM inequality
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For $\mathcal A\subseteq[n]^{(r)}$, the local LYM inequality says
$$
\frac{|\partial\mathcal A|}{\binom n{r-1}}
\geq\frac{|\mathcal A|}{\binom nr}.
$$
It follows by counting pairs $(B,A)$ with $B\subset A$, $|B|=r-1$, and $A\in\mathcal A$.

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