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Rational Ehrhart quasi-polynomials

by Linke, E..

Series: 2010-26, Preprints

52C07 Lattices and convex bodies in $n$ dimensions
11P21 Lattice points in specified regions
11H06 Lattices and convex bodies

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 and 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.

Ehrhart polynomials, Lattice points, Rational polytopes