Abstract
The generating function F(P)=∑α∈P∩ZNxα for a rational polytope P carries all essential information of P. In this paper we show that for any positive integer n, the generating function F(P, n) of nP={nx:x∈P} can be written as F(P, n)=∑α∈APα(n)xnα, where A is the set of all vertices of P and each Pα(n) is a certain periodic function of n. The Ehrhart reciprocity law follows automatically from the above formula. We also present a formula for the coefficients of Ehrhart polynomials in terms of elementary symmetric functions.
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