English

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.

Keywords

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

R2 v1 2026-06-21T15:42:25.166Z