Linear paths and trees in uniform hypergraphs

|F|>(n−1k−1)+(n−2k−1)+⋯+(n−tk−1), then it contains a linear path of length 2t+1. The only extremal family consists of all edges meeting a given t-set. We also determine exk(n,P2t(k)) exactly, and the Turán number of any linear tree asymptotically.