On integer points in polyhedra: A lower bound
Received: 21 April 1989 Revised: 12 March 1991 DOI:
Cite this article as: Bárány, I., Howe, R. & Lovász, L. Combinatorica (1992) 12: 135. doi:10.1007/BF01204716 Abstract
Given a polyhedron
P⊂ℝ we write P for the convex hull of the integral points in I P. It is known that P can have at most I 135-2 vertices if P is a rational polyhedron with size φ. Here we give an example showing that P can have as many as Ω(ϕ I vertices. The construction uses the Dirichlet unit theorem. n−1) AMS subject classification code (1991) 52 C 07 11 H 06
The results of the paper were obtained while this author was visiting the Cowles Foundation at Yale University
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