From Steinitz to Karu: The cd-index

Margaret Readdy

Monday, February 14, 2005
4 pm, 945 Patterson Office Tower

Abstract:

The cd-index is a noncommutative polynomial which encodes all the face incidence information of a polytope, and more generally, the chains in an Eulerian poset. The beauty of this polynomial is that it removes all the linear relations holding among the face data (such as Euler-Poincare). Amazingly, geometric operations performed on a polytope correspond to algebraic operations applied to its cd-index. Stanley has conjectured that the cd-index has nonnegative coefficients for Gorenstein* lattices. Billera and Ehrenborg proved this in the case of face lattices of polytopes. Karu has recently settled Stanley's conjecture, and will talk about his work later this week.

This talk will serve as an introduction to the cd-index for Kalle Karu's colloquium talk later this week.