Constant-intersection family bound
= Constant-intersection family bound
{title2=$|\mathcal F|\leq n\quad(\lambda>0)$}
If distinct members of a <set family> on $[n]$ have intersection size $\lambda$, then its size is at most $n$ for $\lambda>0$, and at most $n+1$ for $\lambda=0$, assuming $n\geq1$. In the positive case, use the <Gram matrix> of the <characteristic vectors of sets>; a member of size $\lambda$ is handled by disjoint remainders. In the zero case nonempty members are disjoint.