Abstract
In this paper, we characterize self-dual elements of a free distributive lattice with n generators by means of a median operation on this lattice. Hence, we obtain a constructive characterization of Sperner's families, for which H is equal to Tr H . We construct some infinite sequences of these families. These results generalize those of N. M. Rivière ( J. Combinatorial Theory 5 (1968), 229–234) and are related to many questions in Boolean algebra, combinatorics, and decision theory.
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