We study the uniqueness of minimal liftings of cut generating functions obtained from maximal lattice-free polytopes. We prove a basic invariance property of unique minimal liftings for general maximal lattice-free polytopes. This generalizes a previous result by Basu, Cornuéjols and Köppe [3] for simplicial maximal lattice-free polytopes, thus completely settling this fundamental question about lifting. We also extend results from [3] for minimal liftings in maximal lattice-free simplices to more general polytopes. These nontrivial generalizations require the use of deep theorems from discrete geometry and geometry of numbers, such as the Venkov-Alexandrov-McMullen theorem on translative tilings, and McMullen’s characterization of zonotopes.


Integer Point Relative Interior Tile Space Unimodular Transformation Nontrivial Generalization 
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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Gennadiy Averkov
    • 1
  • Amitabh Basu
    • 2
  1. 1.Institute of Mathematical Optimization, Faculty of MathematicsUniversity of MagdeburgGermany
  2. 2.Department of Applied Mathematics and StatisticsThe Johns Hopkins UniversityUSA

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