Whitney Numbers of Geometric Lattices

Publisher Summary This chapter discusses Whitney numbers of geometric lattices. There is a homology theory on the category of ordered sets such that the Betti numbers of a geometric lattice are the Whitney numbers of the first kind. The chapter describes such a theory. The theory is a sheaf cohomology on a topological space associated to the ordered set. It is, however, also possible to develop the theory in terms of specific simplicial chain complexes.