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The complex of maximal lattice free simplices

In: Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research

Author

Listed:
  • Imre Bárány

    (Mathematical Institute)

  • Roger Howe

    (Yale University)

  • Herbert E. Scarf

    (Yale University)

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.

Suggested Citation

  • Imre Bárány & Roger Howe & Herbert E. Scarf, 2008. "The complex of maximal lattice free simplices," Palgrave Macmillan Books, in: Zaifu Yang (ed.), Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research, chapter 8, pages 155-163, Palgrave Macmillan.
    • Handle: RePEc:pal:palchp:978-1-137-02441-1_8
    DOI: 10.1057/9781137024411_8
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    Cited by:

    1. I. Bárány & H. E. Scarf & D. Shallcross, 2008. "The topological structure of maximal lattice free convex bodies: The general case," Palgrave Macmillan Books, in: Zaifu Yang (ed.), Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research, chapter 11, pages 191-205, Palgrave Macmillan.
    2. Imre Bárány & Herbert Scarf, 2008. "Matrices with Identical Sets of Neighbors," Palgrave Macmillan Books, in: Zaifu Yang (ed.), Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research, chapter 10, pages 179-189, Palgrave Macmillan.

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