A graded partially ordered set is Eulerian if every interval has the same
number of elements of even rank and of odd rank. Face lattices of convex
polytopes are Eulerian. For Eulerian partially ordered sets, the flag vector
can be encoded efficiently in the cd-index. The cd-index of a polytope has all
positive entries. An important open problem is to give the broadest natural
class of Eulerian posets having nonnegative cd-index. This paper completely
determines which entries of the cd-index are nonnegative for all Eulerian
posets. It also shows that there are no other lower or upper bounds on
cd-coefficients (except for the coefficient of c^n)
