Integral boundary points of convex polyhedra

Abstract

Here is the story of how this paper was written. (a) Independently, Alan and Joe discovered this easy theorem: if the right hand side consists of integers, and if the matrix is totally unimodular, then the vertices of the polyhedron defined by the linear inequalities will all be integral. This is easy to prove and useful. As far as we know, this is the only part of our theorem that anyone has ever used. © 2010 Springer-Verlag Berlin Heidelberg.