Simplex Stability

A d -simplex is a collection of d + 1 sets such that every d of them has non-empty intersection and the intersection of all of them is empty. Fix k ≥ d + 2 ≥ 3 and let be a family of k -element subsets of an n -element set that contains no d -simplex. We prove that if $|\cG| \geq (1 - o(1))\binom{n-... View More