Title

On Integer Points in Polyhedra: A Lower Bound

Document Type

Discussion Paper

Publication Date

6-1-1989

CFDP Number

917

CFDP Pages

12

Abstract

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

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