Ehrhart polynomials of lattice-face polytopesAlgebra & Discrete Mathematics
|Fu Liu, MIT
|Thu, Jan 5 2006, 12:10PM
There is a simple formula for the Ehrhart polynomial of a cyclic polytope. In this talk, we will explain that the same formula holds for a more general class of polytopes, lattice-face polytopes. We develop a way of decomposing any d-dimensional simplex in general position into d! signed sets and carefully count the number of lattice points inside them. We are thus able to conclude the desired formula.