On the number of integer points in translated and expanded polyhedra

05/09/2018

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by   Danny Nguyen, et al.

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We prove that the problem of minimizing the number of integer points inparallel translations of a rational convex polytope in R^6 is NP-hard. We apply this result to show that given a rational convex polytope P ⊂R^6, finding the largest integer t s.t. the expansion tP contains fewer than k integer points is also NP-hard. We conclude that the Ehrhart quasi-polynomials of rational polytopes can have arbitrary fluctuations.