Let p = (p_{1},...,p_{n}) be a vector of positive integers whose greatest common divisor is unity. The Frobenius problem is to find the largest integer f* which cannot be written as a non-negative integral combination of the p_{i}.In this note we relate the Frobenius problem to the topic of...

We present two arguments, one based on index theory, demonstrating that the multi-country Ricardo model has a unique competitive equilibrium if the aggregate demand functions exhibit gross substitutability. The result is somewhat surprising because the assumption of gross substitutability is...

In recent years many advances have been made in solution techniques for specially structured 0-1 integer programming problems. In contrast, very little progress has been made on solving general (mixed integer) problems. This, of course, is not true when viewed from the theoretical side: Lenstra...

Given a generic m x n matrix A, the simplicial complex {bold K}(A) is defined to be the collection of simplices representing maximal lattice point free convex bodies of the form {x : Ax = b}. The main result of this paper is that the topological space associated with {bold K}(A) is homeomorphic...

Tjalling C. Koopmans made fundamental contributions to economics. This paper, prepared for a National Academy of Sciences volume of memoirs, provides a biographical sketch of this extraordinary individual.