DIMACS TR: 93-42

On a Covering Property of Maximal Sperner Families

Authors: Peter L. Erdos and Niall Graham


In the lattice of subsets of an n-set X, every maximal Sperner family S may be partitioned into disjoint subfamilies A and B, such that the union of the upset of A with the downset of B yields the entire lattice: U(A) u D(B) = P(X). The result generalizes to certain posets.

Paper available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1993/93-42.ps
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