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The Topological Structure of Maximal Lattice Free Convex Bodies: The General Case

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Author Info
Imre Barany (Mathematical Institute, Budapest)
Herbert E. Scarf () (Cowles Foundation, Yale University)
David F. Shallcross

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Abstract

Given a generic m x n matrix A, the simplicial complex {bold K}(A) is defined to be the collection of simplices representing maximal lattice point free convex bodies of the form {x : Ax <= b}. The main result of this paper is that the topological space associated with {bold K}(A) is homeomorphic with R^{m-1}.

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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1087.

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Length: 17 pages
Date of creation: Dec 1994
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Publication status: Published in Mathematical Programming (1998), 80: 1-15
Handle: RePEc:cwl:cwldpp:1087

Note: CFP 959.
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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Scarf, Herbert E, 1981. "Production Sets with Indivisibilities-Part I: Generalities," Econometrica, Econometric Society, vol. 49(1), pages 1-32, January. [Downloadable!] (restricted)
  2. Herbert E. Scarf, 1977. "An Observation on the Structure of Production Sets with Indivisibilities," Cowles Foundation Discussion Papers 453, Cowles Foundation, Yale University. [Downloadable!]
  3. Herbert E. Scarf & R. Kannan & Laszlo Lovasz, 1988. "The Shapes of Polyhedra," Cowles Foundation Discussion Papers 883, Cowles Foundation, Yale University. [Downloadable!]
  4. Imre Barany & Roger Howe & Herbert E. Scarf, 1992. "The Complex of Maximal Lattice Free Simplices," Cowles Foundation Discussion Papers 1032, Cowles Foundation, Yale University. [Downloadable!]
  5. 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:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Imre Barany & Herbert E. Scarf, 1996. "Matrices with Identical Sets of Neighbors," Cowles Foundation Discussion Papers 1127, Cowles Foundation, Yale University. [Downloadable!]
  2. 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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