##
The cd-index of an Eulerian poset

**Nathan Reading**

University of Minnesota

Abstract: In this talk we will discuss various bases for
the flag

f-vectors of Eulerian posets. (Eulerian posets include, for example,
face

lattices of convex polytopes and intervals in the strong Bruhat order).

In particular we will define the cd-index, a non-commutative polynomial

which compactly encodes the flag f-vector. The cd-index is conjectured

to have non-negative coefficients for any poset whose order complex
is a

homology sphere. Using a series of basis changes, we can "lift"
a trivial

convolution formula on flag f-vectors to a convolution formula on

cd-coefficients, leading to partial results on the non-negativity

conjecture. If time allows, we will also discuss the partial
orders which

mediate many of the basis changes. These are natural partial
orders whose

groundsets are counted by the Fibonacci numbers.