Maximal s -wise t -intersecting families of sets: kernels, generating sets, and enumeration

摘要: Abstract A family of k-subsets an n-set is said to be s-wise t-intersecting if |A1∩…∩As|⩾t, for any A1, …, As∈ . For fixed s, n, k, and t, let Is(n, k, t) denote the set all such families. ∈Is(n, k, t) maximal it not properly contained in other Is(n, k, t). We show that s, k, t, there integer n0=n0(k, s, t), which families Is(n0, k, t) completely determine Is(n, k, t), n⩾n0. give a construction Is(n+1, k+1, t+1) based on those Finally, s=2, we classify k=t+1, n⩾t+2, t⩾1, k=t+2, n⩾t+6, t⩾1. The concepts kernels generating sets subsets play important role this work.