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Estimating the Number of Lattice Points in a Convex Polytope

Faculty Mentor: Dr. Steven Rosenberg, Mathematics

ABSTRACT: We will give some estimates for the number of lattice points in a convex polytope, which is described by a system of linear inequalities. We restate a result of Rosenberg [1] on orthogonal arrays using convex polytopes, and find that the number of orthogonal arrays is equal to the number of lattice points in a certain polytope. We examine methods for determining the number of lattice points in a polytope. We also find the volume of certain highly symmetric polytopes.

Last modified: Monday March 03 2008
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