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In honor of Joel Spencer's 60+ birthday For k-uniform hypergraphs F and H and an integer r ≥ 2, let c r,F (H) denote the number of r-colorings of the set of hyperedges of H with no monochromatic copy of F and let c r,F (n) = max H∈Hn c r,F (H), where the maximum runs over the family H n of all k-uniform hypergraphs on n vertices. Moreover, let ex(n, F ) be the usual Turán function, i.e., the maximum number of hyperedges of an n-vertex k-uniform hypergraph which contains no copy of F . In thisdoi:10.4310/joc.2010.v1.n4.a4 fatcat:s3lyjqrrvvcpxhgodol6fprpae