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The Frobenius Problem and Maximal Lattice Free Bodies

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Author Info
Herbert E. Scarf () (Cowles Foundation, Yale University)
Shallcross, David F. (Thomas J. Watson Research Center, IBM)

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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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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 945.

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Length: 12 pages
Date of creation: Jun 1990
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Publication status: Published in Mathematics of Operation Research (August 1993), 18(3): 511-515
Handle: RePEc:cwl:cwldpp:945

Note: CFP 892.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Algorithm; Frobenius problem;

References listed on IDEAS
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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. [Downloadable!] (restricted)
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Cited by:
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  1. Herbert E. Scarf & Kevin M. Woods, 2004. "Neighborhood Complexes and Generating Functions for Affine Semigroups," Cowles Foundation Discussion Papers 1458, Cowles Foundation, Yale University. [Downloadable!]
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