Diameter of a set family
= Diameter of a set family
{title2=$\operatorname{diam}(\mathcal F)=\max_{A,B\in\mathcal F}|A\triangle B|$}
= Hamming diameter
{c}
{synonym}
This is the maximum Hamming distance between the characteristic vectors of members of a set family. In a down-set, one can replace a pair by disjoint subsets with the same union, so the maximum distance equals the largest size of a union of two members. A t-intersecting family has diameter at most $n-t$.