Experimental study of the Ehrhart interpolation polytope

Abstract

In this paper we define a family of polytopes called Ehrhart Interpolation Polytopes with respect to a given polytope and a parameter corresponding to the dilation of the polytope. We experimentally study the behavior of the number of lattice points in each member of the family, looking for a member with a single lattice point. That single lattice point is the h* vector of the given polytope. Our study is motivated by efficient algorithms for lattice point enumeration. © 2018 Elsevier B.V., All rights reserved.