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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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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d09/d0945.pdf
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    1. Scarf, Herbert E, 1981. "Production Sets with Indivisibilities-Part II: The Case of Two Activities," Econometrica, Econometric Society, vol. 49(2), pages 395-423, March.
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    Cited by:

    1. Herbert E. Scarf & Kevin M. Woods, 2004. "Neighborhood Complexes and Generating Functions for Affine Semigroups," Cowles Foundation Discussion Papers 1458, Cowles Foundation for Research in Economics, Yale University.

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    Keywords

    Algorithm; Frobenius problem;

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