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Mathematical Programming

, Volume 80, Issue 1, pp 1–15 | Cite as

The topological structure of maximal lattice free convex bodies: The general case

  • I. Bárány
  • H. E. Scarf
  • D. Shallcross
Article

Abstract

Given a genericm × n matrixA, the simplicial complexK(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 withK(A) is homeomorphic withR m−1 . © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

Keywords

Minimal test sets for integer programming Simplicial complexes Maximal lattice free bodies 

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Copyright information

© The Mathematical Programming Society, Inc 1998

Authors and Affiliations

  • I. Bárány
    • 1
  • H. E. Scarf
    • 2
  • D. Shallcross
    • 3
  1. 1.Mathematical InstituteBudapestHungary
  2. 2.Cowles Foundation for Research in EconomicsYale UniversityNew HavenUSA
  3. 3.BellcoreMorristownUSA

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