Multidimensional Ehrhart reciprocity (Q1604579)

Using a generalization of Ehrhart's idea of counting lattice polytopes in dilated rational polytopes, the author proved in an earlier paper [Electron. J. Comb. 6, No. 1, Research paper R37, 9 p. (1999; Zbl 0934.11048)] that, if the rational polytope is a simplex, the number of lattice points in the interior and closure of a vector-dilated simplex (i.e. a simplex where one uses different dilation factors for each of the facets) are quasipolynomials satisfying an Ehrhart-type reciprocity law. In this paper the author extends this result to general rational polytopes. Moreover, as a corollary, he obtains a generalization of a reciprocity theorem of Stanley.