COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 945

"The Frobenius Problem and Maximal Lattice Free Bodies"

Herbert E. Scarf and David Shallcross

June 1990

Let p = (p₁,...,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 maximal lattice free bodies and describe an algorithm for n = 3.

Keywords: Algorithm, Frobenius problem

JEL Classification: 213