Discrete Geometry and Combinatorics Seminar
A poset is Eulerian if it is graded and every non-trivial interval satisfies the Euler-PoincarŽ relation. After describing examples stemming from polytopes, regular CW-complexes and the strong Bruhat order on Coxeter groups, we will review the cd-index. This non-commutative polynomial has emerged as a useful tool for studying face incidence structure data. We then discuss Gustafson's new method to form an Eulerian poset from a generator enriched lattice called the strong minor poset. Finally, Ehrenborg, Goresky and I relax the Eulerian condition so that it holds for Whitney stratified manifolds. This topologically cognizant setting allows us to generalize the research program of characterizing face vectors of polytopes. This talk is suitable for a general audience.