Powers of tight Hamilton cycles in randomly perturbed hypergraphs

For k ≥ 2 and r ≥ 1 such that k + r ≥ 4, we prove that, for any α > 0, there exists ε > 0 such that the union of an n-vertex k-graph with minimum codegree (Formula presented.) and a binomial random k-graph (Formula presented.) with (Formula presented.) on the same vertex set contains the rth power of a tight Hamilton cycle with high probability. This result for r = 1 was first proved by McDowell and Mycroft.