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Rational Ehrhart quasi-polynomials. (English) Zbl 1234.52010

Summary: Ehrhart’s famous theorem states that the number of integral points in a rational polytope is a quasi-polynomial in the integral dilation factor. We study the case of rational dilation factors. It turns out that the number of integral points can still be written as a rational quasi-polynomial. Furthermore, the coefficients of this rational quasi-polynomial are piecewise polynomial functions and related to each other by derivation.

MSC:

52B20 Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry)
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