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On Integer Points in Polyhedra: A Lower Bound

Author

Listed:
  • Imre Barany

    (Mathematical Institute, Budapest)

  • Roger Howe

    (Dept. of Mathematics, Yale University)

  • Laszlo Lovasz

    (Eotvos & Princeton Universities)

Abstract

Given a polyhedron we write P(I) for the convex hull of the integral points in P. It is know that P(I) can have at most O(fi(n-1)) vertices if P is a rational polyhedron with size fi. Here we give an example showing that P(I) can have as many as Omega (fi(n-1)) vertices. The construction uses the Dirichlet unit theorem.

Suggested Citation

  • Imre Barany & Roger Howe & Laszlo Lovasz, 1989. "On Integer Points in Polyhedra: A Lower Bound," Cowles Foundation Discussion Papers 917, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:917
    as

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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d09/d0917.pdf
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    References listed on IDEAS

    as
    1. David S. Rubin, 1970. "On the Unlimited Number of Faces in Integer Hulls of Linear Programs with a Single Constraint," Operations Research, INFORMS, vol. 18(5), pages 940-946, October.
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    Cited by:

    1. Herbert E. Scarf & Shallcross, David F., 1991. "Shortest Integer Vectors," Cowles Foundation Discussion Papers 965, Cowles Foundation for Research in Economics, Yale University.

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