2 problems

A $(j,i)$-configuration in a family of sets is a collection of $i$ members spanning at most $j$ ground-set elements; the girth of a triangle packing is the smallest $i\geq 2$ for w…

A Steiner system with parameters $(n,q,r)$ is a design in which every $r$-subset belongs to exactly one $q$-subset. For a partial $(n,q,r)$-Steiner system, the girth is the smalles…