TITLE: Positivity of Ehrhart polynomial coefficients
QUESTION [8 upvotes]: Are there any results stating that a given family of convex polytopes have Ehrhart polynomials with non-negative coefficients?
What methods are available for proving such a property for some family of polytopes?
Remember, the Ehrhart polynomial $p(k)$ for a convex polytope $P$ with integer vertices is given by the property that $p(k)$ counts the number of integer lattice points in the $k$-dilation of $P$, where $k$ is a positive integer.

REPLY [3 votes]: Fu Liu recently put on the arXiv a nice survey about this question: https://arxiv.org/abs/1711.09962v1