Lubell--Yamamoto--Meshalkin inequality
= Lubell--Yamamoto--Meshalkin inequality
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{wiki=Lubell–Yamamoto–Meshalkin_inequality}
If $\mathcal A$ is an antichain in $\mathcal P([n])$ and $\mathcal A_h$ is its rank-$h$ part, then
$$
\sum_{h=0}^n\frac{|\mathcal A_h|}{\binom nh}\leq1.
$$
The left side is the expected number of members of $\mathcal A$ on a <Uniformly random maximal chain in a Boolean lattice>.
= LYM inequality
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{synonym}