Rational Ehrhart quasi-polynomials

by E. Linke


Preprint series: 10-26

52C07 Lattices and convex bodies in $n$ dimensions, See Also {11H06, 11H31, 11P21}
11P21 Lattice points in specified regions
11H06 Lattices and convex bodies, See also {11P21, 52C05, 52C07}

Abstract: 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.

Keywords: Ehrhart polynomials, Lattice points, Rational polytopes

Notes: Supported by the Deutsche Forschungsgemeinschaft within the project He 2272/4-1

Upload: 2010-07-02

Update: 2011-01-18


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