Formulas of Brion, Lawrence, and Varchenko on rational generating functions for cones. (Q1000914)

In this paper, the authors consider formulas of Brion, Lawrence and Varchenko, which express the generating function of (integer points inside) some polytope \(P\) as a signed sum of generating functions of certain cones derived from \(P\), and show how these formulas can be proved by counting arguments. Moreover, they outline a uniform proof for these formulas (based on the polar of a polyhedron).