All Outputs (2)

Roots of Ehrhart polynomials of smooth Fano polytopes (2011)
Journal Article
Hegedüs, G., & Kasprzyk, A. M. (2011). Roots of Ehrhart polynomials of smooth Fano polytopes. Discrete and Computational Geometry, 46(3), https://doi.org/10.1007/s00454-010-9275-y

V. Golyshev conjectured that for any smooth polytope P of dimension at most five, the roots $z\in\C$ of the Ehrhart polynomial for P have real part equal to -1/2. An elementary proof is given, and in each dimension the roots are described explicitly.... Read More about Roots of Ehrhart polynomials of smooth Fano polytopes.

The boundary volume of a lattice polytope (2011)
Journal Article
Hegedüs, G., & Kasprzyk, A. M. (2011). The boundary volume of a lattice polytope. Bulletin of the Australian Mathematical Society, 85(1), https://doi.org/10.1017/S0004972711002577

For a d-dimensional convex lattice polytope P, a formula for the boundary volume vol(δP) is derived in terms of the number of boundary lattice points on the first [d/2] dilations of P. As an application we give a necessary and sufficient condition fo... Read More about The boundary volume of a lattice polytope.