Note on the Coefficients of Rational Ehrhart Quasi-polynomials of Minkowski-sums
نویسنده
چکیده
By extending former results of Ehrhart, it was shown by Peter McMullen that the number of lattice points in the Minkowski-sum of dilated rational polytopes is a quasipolynomial function in the dilation factors. Here we take a closer look at the coefficients of these quasi-polynomials and show that they are piecewise polynomials themselves and that they are related to each other by a simple differential equation. As a corollary, we obtain a refinement of former results on lattice points in vector dilated polytopes.
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