### 2010-26

by Linke, E..

**Series:** 2010-26, Preprints

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

**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