ChenBeifang

This talk is about the chromatic and flow polynomials from the viewpoint of counting lattice points. First, I present Stanley's interpretation for the values of the chromatic polynomial at negative integers. Next, it is generalized to the flow polynomials by interpreting the values of the flow polynomial at negative integers. After that I will present the duality between the chromatic polynomial and the flow polynomial of a graph embedded on an oriented surface. The method of counting lattice points and the Ehrhart polynomials may be applied to study other polynomials arising in combinatorics.