# Rational Ehrhart Theory

@inproceedings{Beck2021RationalET, title={Rational Ehrhart Theory}, author={Matthias Beck and Sophia Elia and Sophie Rehberg}, year={2021} }

The Ehrhart quasipolynomial of a rational polytope P encodes fundamental arithmetic data of P, namely, the number of integer lattice points in positive integral dilates of P. Ehrhart quasipolynomials were introduced in the 1960s, satisfy several fundamental structural results and have applications in many areas of mathematics and beyond. The enumerative theory of lattice points in rational (equivalently, real) dilates of rational polytopes is much younger, starting with work by Linke (2011…

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It is shown that the period of the Ehrhart quasipolynomial of these polytopes is at most 2 if the graph is a tree or a cubic graph, and it is equal to 4 otherwise.

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