Flag Numbers of Polytopes and Partially Ordered Sets
Abstract: The f-vector of a convex polytope gives the number of i-dimensional faces of the polytope for all i. The problem of characterizing the f-vectors of all polytopes has proved intractable. More combinatorial information is encoded in the flag vector, a useful extension of the f-vector. In this talk I will define flag vectors, the cd-index and Eulerian posets, and will survey results on linear inequalities.