, Volume 12, Issue 2, pp 135–142 | Cite as

On integer points in polyhedra: A lower bound

  • Imre Bárány
  • Roger Howe
  • László LovászEmail author


Given a polyhedronP⊂ℝ we writePI for the convex hull of the integral points inP. It is known thatPI can have at most135-2 vertices ifP is a rational polyhedron with size φ. Here we give an example showing thatPI can have as many as Ω(ϕn−1) vertices. The construction uses the Dirichlet unit theorem.

AMS subject classification code (1991)

52 C 07 11 H 06 


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Copyright information

© Akadémiai Kiadó 1992

Authors and Affiliations

  1. 1.Mathematical InstituteBudapestHungary
  2. 2.Department of MathematicsYale UniversityNew HavenU.S.A.
  3. 3.Department of Computer ScienceEötvös UniversityBudapestHungary

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