On integer points in polyhedra: A lower bound

Imre Bárány, Roger Howe, László Lovász

Research output: Contribution to journalArticle

23 Citations (Scopus)


Given a polyhedron P⊂ℝ we write PI for the convex hull of the integral points in P. It is known that PI can have at most 135-2 vertices if P is a rational polyhedron with size φ. Here we give an example showing that PI can have as many as Ω(φ{symbol}n-1) vertices. The construction uses the Dirichlet unit theorem.

Original languageEnglish
Pages (from-to)135-142
Number of pages8
Issue number2
Publication statusPublished - Jun 1 1992


  • AMS subject classification code (1991): 52C07, 11H06

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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