The maximum size of 4-wise 2-intersecting and 4-wise 2-union families (Q2493102)

The following variation of the Erdős-Ko-Rado theorem is proved: Let \( \mathcal{F}\) be an \(n\)-uniform hypergraph on \(2n\) vertices. Suppose that \( \left| F_{1}\cap F_{2}\cap F_{3}\cap F_{4}\right| \geq 2\) and \( \left| F_{1}\cup F_{2}\cup F_{3}\cup F_{4}\right| \leq n-2\) hold for all \(F_{1},F_{2},F_{3},F_{4}\in \mathcal{F}\). Then the size of \(\mathcal{F}\) is at most \(\binom{2n-4}{n-2}\) for \(n\) sufficiently large.