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The Frobenius Problem and Maximal Lattice Free Bodies

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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.

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  • Herbert E. Scarf & Shallcross, David F., 1990. "The Frobenius Problem and Maximal Lattice Free Bodies," Cowles Foundation Discussion Papers 945, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:945
    Note: CFP 892.
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    1. H. W. Lenstra, 1983. "Integer Programming with a Fixed Number of Variables," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 538-548, November.
    2. Herbert E. Scarf, 2008. "Production Sets with Indivisibilities Part II. The Case of Two Activities," Palgrave Macmillan Books, in: Zaifu Yang (ed.), Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research, chapter 3, pages 39-67, Palgrave Macmillan.
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    1. Herbert E. Scarf & Kevin M. Woods, 2008. "Neighborhood Complexes and Generating Functions for Affine Semigroups," Palgrave Macmillan Books, in: Zaifu Yang (ed.), Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research, chapter 12, pages 207-225, Palgrave Macmillan.

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    Keywords

    Algorithm; Frobenius problem;

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