Triple Systems Not Containing a Fano Configuration

Given a 3-uniform hypergraph F , let ex3(n,F) denote the maximum possible size of a 3-uniform hypergraph of order n that does not contain any subhypergraph isomorphic to F . Our terminology follows that of [16] and [10], which are comprehensive survey articles of Turán-type extremal graph and hypergraph problems, respectively. Also see the monograph of Bollobás [2]. There is an extensive literature on Extremal Graph Problems. Nevertheless, we know much less about the hypergraph extremal problems and we have even fewer exact results on hypergraphs. One of the main contributions of this paper is that we improve an earlier result of de Caen and Füredi [5], providing the exact solution of the Fano hypergraph extremal problem.