On counting integral points in a convex rational polytope
Given a convex rational polytope $\Omega(b):=\{x\in\R^n_+\,|\,Ax=b\}$, we consider the function $b\mapsto f(b)$, which counts the nonnegative integral points of $\Omega(b)$. A closed form expression of its $\Z$-transform $z\mapsto \mathcal{F}(z)$ is easily obtained so that $f(b)$ can be computed as the inverse $\Z$-transform of $\mathcal{F}$. We then provide two variants of an inversion algorithm. As a … Read more