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The Frobenius Problem and Maximal Lattice Free Bodies

By Herbert E. Scarf and David F. Shallcross

Abstract

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 maximal lattice free bodies and describe an algorithm for n = 3.Algorithm, Frobenius problem

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