= Weighted intersecting family bound on an odd Boolean lattice
{title2=$\sum_{S\in\mathcal F}w^{|S|}\leq\sum_{r>n/2}\binom nr w^r$}
For odd $n$ and $w\geq1$, an <intersecting family> contains at most one set from each complementary pair in the <Boolean lattice>. Choosing the larger member in every pair gives the displayed bound and is feasible, because all sets of size greater than $n/2$ intersect. For $w>1$ it is the unique maximizer; for $w=1$ other maximizing families can exist.
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