Lattice vertex polytopes with interior lattice points

Douglas Austin Hensley

Vol. 105 (1983), No. 1, 183–191

DOI: 10.2140/pjm.1983.105.183

Abstract

Consider a convex polytope with lattice vertices and at least one interior lattice point. We prove that the number of boundary lattice points is bounded above by a function of the dimension and the number of interior lattice points. This extends to arbitrary dimension a result of Scott for the two dimensional case.

Mathematical Subject Classification

Primary: 52A43, 52A43

Secondary: 10E05

Milestones

Received: 28 May 1981

Revised: 2 November 1981

Published: 1 March 1983