Turán numbers of extensions

The extension of an r-uniform hypergraph G is obtained from it by adding for every pair of vertices of G, which is not covered by an edge in G, an extra edge containing this pair and (r−2) new vertices. Keevash [3] and Sidorenko [9] have previously determined Turán densities of two families of hypergraph extensions. We determine the Turán numbers for these families, using classical stability techniques and new tools introduced in [5].