10-26
Rational Ehrhart quasi-polynomials
by E. Linke
Preprint series: 10-26
- MSC:
- 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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