Multiply intersecting families of sets
This paper studies \(r\)-wise \(s\)-intersecting set systems on an \(n\)-element underlying set, where there is also an upper size-restriction on the intersections: the cardinality of the intersection of any \(l\) sets is at most \(t.\) The authors prove a tight upper bound \((l-1)n\) for the case \(s=1\) and \(l=1.\) They also give the asymptotic solution for the general case.
\(r\)-wise \(s\)-intersecting set systems
scientific article; zbMATH DE number 2082026