Let n,k,r and t be positive integers, and let [n] = {1,2, . . . ,n}. A family G ⊂ 2[n] is called r-wise t-intersecting if |G1∩·· ·∩Gr| ≥ t holds for all G1, . . . ,Gr ∈ G . Let us define a typical r-wise t-intersecting family Gi(n,r, t) and its k-uniform subfamily Fi(n,k,r, t), where 0 ≤ i ≤ ⌊n−t r ⌋, as follows: Gi(n,r, t) = {G ⊂ [n] : |G∩ [t + ri]| ≥ t +(r−1)i}, Fi(n,k,r, t) = Gi(n,r, t)∩ ([n...
