Lower bounds on the coefficients of Ehrhart polynomials

@article{Henk2009LowerBO,
  title={Lower bounds on the coefficients of Ehrhart polynomials},
  author={Martin Henk and Makoto Tagami},
  journal={Eur. J. Comb.},
  year={2009},
  volume={30},
  pages={70-83}
}
We present lower bounds for the coefficients of Ehrhart polynomials of convex lattice polytopes in terms of their volume. We also introduce two formulas for calculating the Ehrhart series of a kind of a ”weak” free sum of two lattice polytopes and of integral dilates of a polytope. As an application of these formulas we show that Hibi’s lower bound on the coefficients of the Ehrhart series is not true for lattice polytopes without interior lattice points. 

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