On a Covering Property of Maximal Sperner Families
Authors: Peter L. Erdos and Niall Graham
ABSTRACT
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.
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