Abstract
We determine the asymptotics of the largest family of qualitatively 2-independentk-partitions of ann-set, for everyk>2. We generalize a Sperner-type theorem for 2-partite sets of Körner and Simonyi to thek-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.
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Work supported in part by the Italian Ministry of the University and of the Scientific Research in the framework of the “Algoritmi e Sistemi di Calcolo” project.
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Gargano, L., Körner, J. & Vaccaro, U. Sperner capacities. Graphs and Combinatorics 9, 31–46 (1993). https://doi.org/10.1007/BF01195325
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DOI: https://doi.org/10.1007/BF01195325