"Sweeping the cd-Index"

Carl Lee
University of Kentucky

Monday, September 17, 2007
4:00 pm, 113 Patterson Office Tower

Abstract:

The cd-index of a convex polytope concisely encodes information about the flag-vector of the polytope --- the numbers of chains of faces of all types. Stanley proved that the coefficients of the cd-index are non-negative using the technique of S-shellings. By interpreting an S-shelling of a polytope P in the context of its dual P^* we provide a simple recursive way to compute the cd-index by sweeping a hyperplane across P^*. In addition we offer a way to visualize a partition of the flags of P^* into subsets counted by the coefficients of the cd-index. Finally, we show how also the toric h-vector can be easily computed from a hyperplane sweep, and hence directly from the cd-index.