COEFFICIENTS AND ROOTS OF EHRHART POLYNOMIALS

@article{Beck2003COEFFICIENTSAR,
  title={COEFFICIENTS AND ROOTS OF EHRHART POLYNOMIALS},
  author={Matthias Beck and Jes{\'u}s A. De Loera and Mike Develin and Julian Pfeifle and Richard P. Stanley},
  journal={arXiv: Combinatorics},
  year={2003},
  pages={15-36}
}
The Ehrhart polynomial of a convex lattice polytope counts integer points in integral dilates of the polytope. We present new linear inequalities satisfied by the coeffi- cients of Ehrhart polynomials and relate them to known inequalities. We also investigate the roots of Ehrhart polynomials. We prove that for fixed d, there exists a bounded region of C containing all roots of Ehrhart polynomials of d-polytopes, and that all real roots of these polynomials lie in (−d, ⌊d/2⌋). In contrast, we… 

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