The complex of maximal lattice free simplices

Imre Bárány, Roger Howe and Herbert Scarf
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Imre Bárány: Mathematical Institute
Roger Howe: Yale University

Chapter 8 in Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research, 2008, pp 155-163 from Palgrave Macmillan

Abstract: Abstract The simplicial complex K(A) is defined to be the collection of simplices, and their proper subsimplices, representing maximal lattice free bodies of the form (x: Ax⩽b), with A a fixed generic (n +1 ) × n matrix. The topological space associated with K(A) is shown to be homeomorphic to ℝ n , and the space obtained by identifying lattice translates of these simplices is homeorphic to the n-torus.

Keywords: Minimal test sets for integer programming; Simplicial complexes; Maximal lattice free bodies (search for similar items in EconPapers)
Date: 2008
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Working Paper: The Complex of Maximal Lattice Free Simplices (1992)
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Persistent link: https://EconPapers.repec.org/RePEc:pal:palchp:978-1-137-02441-1_8

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DOI: 10.1057/9781137024411_8

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