A Construction of Almost Steiner Systems. Issue 11 (10th November 2013) - Ferber, Asaf
Abstract Let n, k, and t be integers satisfying n>k>t≥2. A Steiner system with parameters t, k, and n is a k‐uniform hypergraph on n vertices in which every set of t distinct vertices is contained in exactly one edge. An outstanding problem in Design Theory is to determine whether a nontrivial Steiner system exists for t≥6. In this note we prove that for every k>t≥2 and sufficiently large n, there exists an almost Steiner system with parameters t, k, and n; that is, there exists a k‐uniform hypergraph on n vertices such that every set of t distinct vertices is covered by either one or two edges.