Sperner Capacities

We determine the asymptotics of the largest family of qualitatively 2-independent k-partitions of an n-set, for every k>2. We generalize a Sperner-type theorem for 2-partite sets of Körner and Simonyi to the k-partite case. Both results have the feature that the corresponding trivial information-theoretic upper bound is tight. The results follow from a more general Sperner capacity theorem for a family of graphs in the sense of our previous work on Sperner theorems on directed graphs