On Integer Points in Polyhedra: A Lower Bound

Imre Barany, Roger Howe and Laszlo Lovasz
Additional contact information
Imre Barany: Mathematical Institute, Budapest
Roger Howe: Dept. of Mathematics, Yale University
Laszlo Lovasz: Eotvos & Princeton Universities

No 917, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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

Keywords: Polyhedra; integral points; Dirichlet unit theorem (search for similar items in EconPapers)
Pages: 12 pages
Date: 1989-05
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Published in Combinatorica (1992), 12(2): 135-142

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