Rational Ehrhart quasi-polynomials

Details Rational Ehrhart quasi-polynomials Rational Ehrhart quasi-polynomials

2010-06-29

arxiv.org/abs/1006.5612v2

Mathematics

Combinatorics

15 pages, several changes in the exposition

Scientific paper

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.

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