Exact computation of the hypergraph Turán function for expanded complete 2-graphs

Let l>k⩾3. Let the k-graph be obtained from the complete 2-graph by enlarging each edge with a new set of k−2 vertices. Mubayi [A hypergraph extension of Turánʼs theorem, J. Combin. Theory Ser. B 96 (2006) 122–134] computed asymptotically the Turán function . Here we determine the exact value of for all sufficiently large n, settling a conjecture of Mubayi.