The Mobius number of a finite partially ordered set equals (up to sign) the difference between the number of even and odd edge covers of its incomparability graph. We use Alexander duality and the nerve lemma of algebraic topology to obtain a stronger result. It relates the homology of a finite simplicial complex Delta that is not a simplex to the cohomology of the complex Gamma of nonempty sets of minimal non-faces that do not cover the vertex set of Delta. (C) 1997 Academic Press.
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