The cd-index of an Eulerian poset is a polynomial in noncommuting variables that is used to encode data on the number of chains within that poset.  I will focus in this talk on a particular class of Eulerian posets involving the Bruhat order of Coxeter groups.  I will use poset operations such as zipping and the pyramid operation to develop Reading's recursive formula for the cd-index of Bruhat intervals.

There are many combinatorial interpretations of Stirling numbers of the first and second kinds. In this talk I will focus on the interpretations of de Medicis and Leroux involving 0-1 tableaux and 0-1 matrices. I will describe how they use them to prove identities involving Stirling numbers, such as orthogonality and Carlitz' identity.

A problem of recent importance has been to identify when a lattice polytope has a symmetric and unimodular h*-vector. In the 1960s, Stanley showed that symmetry occurs exactly when the polytope is Gorenstein. In 2003, Athanasiadis gave sufficient conditions for unimodality.  In this talk, we will discuss a result by Bruns and Römer that generalizes these conditions.