Title: Combinatorics of the Descent Set Polynomial and the Diamond Product

Abstract: In this talk, we will first examine the descent set polynomial, which was defined by Chebikin, Ehrenborg, Pylyavskyy, and Readdy in terms of the descent set statistics of the symmetric group.  We will explain why large classes of cyclotomic polynomials are factors of the descent set polynomial, focusing on instances of the 2pth cyclotomic polynomial for a prime p.  Next, the diamond product of two Eulerian posets will be discussed, particularly the effect this product has on their cd-indices.  A combinatorial interpretation involving weighted lattice paths will be introduced to describe the outcome of applying the diamond product operator to two cd-monomials.