NOTE ON A COMBINATORIAL APPLICATION OF ALEXANDER DUALITY

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 o f algebraic topology to obtain a stronger result. It relates the homol ogy 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.