Reverse Split Rank

  • Michele Conforti
  • Alberto Del Pia
  • Marco Di Summa
  • Yuri Faenza
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8494)


The reverse split rank of an integral polytope P is defined as the supremum of the split ranks of all rational polyhedra whose integer hull is P. Already in ℝ3 there exist polytopes with infinite reverse split rank. We give a geometric characterization of the integral polytopes in ℝ n with infinite reverse split rank.


Convex Hull Linear Subspace Integer Point Discrete Apply Mathematic Rational Polyhedron 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Michele Conforti
    • 1
  • Alberto Del Pia
    • 2
  • Marco Di Summa
    • 1
  • Yuri Faenza
    • 3
  1. 1.Dipartimento di MatematicaUniversità degli Studi di PadovaItaly
  2. 2.Business Analytics and Mathematical Sciences DepartmentIBM Watson Research CenterYorktown HeightsUSA
  3. 3.DISOPTInstitut de mathématiques d’analyse et applications, EPFLSwitzerland

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