Rational Ehrhart quasi-polynomials
Combinatorics
2011-03-04 v2 Metric Geometry
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.
Cite
@article{arxiv.1006.5612,
title = {Rational Ehrhart quasi-polynomials},
author = {Eva Linke},
journal= {arXiv preprint arXiv:1006.5612},
year = {2011}
}
Comments
15 pages, several changes in the exposition