No abstract

A new index for convex polytopes is introduced. It is a vector whose length is the dimension of the linear span of the flag vectors of polytopes. The existence of this index is equivalent to the generalized Dehn-Sommerville equations. It can be computed via a shelling of the polytope. The ranks of the middle perversity intersection homology of the associated toric variety are computed from the index. This gives a proof of a result of Kalai on the relationship between the Betti numbers of a polytope and those of its dual.

No abstract

The closed cone of flag vectors of Eulerian partially ordered sets is studied. A new family of linear inequalities valid for Eulerian flag vectors is given. Half-Eulerian posets are defined. Certain limit posets of Billera and Hetyei are half-Eulerian; they give rise to extreme rays of the cone for Eulerian posets. Other extreme posets are formed from consideration of the cd-index. The cone of Eulerian flag vectors is completely determined up through rank seven.