Margaret M. Bayer - Eulerian partially ordered sets

The face lattices of convex polytopes belong to the class of Eulerian partially ordered sets. In every interval of these ranked posets, the number of elements of even rank equals the number of elements of odd rank. The flag vector of a ranked poset gives the numbers of chains for the various rank sets. This talk discusses the closed convex cone of flag vectors of Eulerian posets. (The linear span is determined by the generalized Dehn-Sommerville equations.) The approach is based on work of Billera and Hetyei on flag vectors of ranked posets and uses ``half-Eulerian'' partially ordered sets.