= Eventown theorem
{c}
{title2=$|\mathcal A|\leq2^{\lfloor n/2\rfloor}$}
If every member of a <set family> on $[n]$ and every distinct pairwise <intersection> has even size, its <characteristic vectors> span a <self-orthogonal binary subspace>. The standard <dot product> is <nondegenerate>, so $W\subseteq W^\perp$ implies $2\dim W\leq n$. Thus the <set family> has at most $2^{\lfloor n/2\rfloor}$ members. All unions of $\lfloor n/2\rfloor$ disjoint pairs of points attain this bound.
Back to article page
