Title:  A Lattice Path Interpretation of the Diamond Product

Abstract:  The diamond product is a poset operation that corresponds to the Cartesian product of polytopes.  The effect the diamond product has on the cd-indices of posets has been previously studied using coproducts, which resulted in recursive formulas for the product of two cd-polynomials and showed that the product is non-negative on cd-indices.  In this talk, I will give a combinatorial interpretation for the diamond product of two cd-monomials that involves weighted lattice paths.