Enumeration of integer projections of parametric polytopes

Although Barvinok's algorithm for counting lattice points in a rational polytope easily extends to linearly parametrized polytopes, it is not immediately obvious whether the same applies to Barvinok and Woods' algorithm for counting the number of points in the integer projection of a polytope. We therefore propose a heuristics based technique that directly manipulates the parametric polytope, reducing it by either eliminating variables, slicing the polyhedron in the combined data and parameter space along a line or ray, or splitting the problem into several smaller subproblems.poster + abstract, pp 71-73 in PA3CT Symposium Proceedingsstatus: publishe