Triangles in r-wise t-intersecting families

Let t, r, k and n be positive integers and F a family of k-subsets of an n-set V. The family F is r-wise t-intersecting if for any F-1, . . . , F-r is an element of F, we have |boolean AND(r)(i=1) F-i| >= t. An r-wise t-intersecting family of r + 1 sets {T-1, . . . , Tr+1} is called an (r + 1, t)-triangle if |T-1 boolean AND center dot center dot center dot boolean AND Tr+1| <= t - 1. In this paper, we prove that if n >= n(0)(r, t, k), then the r-wise t-intersecting family F subset of (([n])(k)) containing the most (r + 1, t)-triangles is isomorphic to {F is an element of(([n])(k)) : |F boolean AND [r + t]| >= r + t - 1}. This can also be regarded k as a generalized Turan type result. (c) 2023 Elsevier Ltd. All rights reserved.