• Corpus ID: 239049878

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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References

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TLDR
An algorithm is provided to compute the resulting Ehrhart quasi-polynomials in the form of explicit step polynomials, which are naturally valid for real (not just integer) dilations and thus provide a direct approach to real EHRhart theory.
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