, Volume 12, Issue 2, pp 135–142

On integer points in polyhedra: A lower bound


  • Imre Bárány
    • Mathematical Institute
  • Roger Howe
    • Department of MathematicsYale University
    • Department of Computer ScienceEötvös University

DOI: 10.1007/BF01204716

Cite this article as:
Bárány, I., Howe, R. & Lovász, L. Combinatorica (1992) 12: 135. doi:10.1007/BF01204716


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 0711 H 06
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© Akadémiai Kiadó 1992