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International Conference on Integer Programming and Combinatorial Optimization

IPCO 1995: Integer Programming and Combinatorial Optimization pp 244–251Cite as

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

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 920))

Abstract

Given a generic m×n matrix A, the simplicial complex 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 K(A) is homeo-morphic with R m −1.

The first author was partially supported by Hungarian NSF grant 1909, the second author by NSF grant SES9121936, and both the first and second author by the program in Discrete Mathematics at Yale University.

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References

  1. I. Bárány, R. Howe, H. E. Scarf: The complex of maximal lattice-free simplices (1993), 3rd IPCO conference, and Math. Progr. 66 (1994), 273–281.

    Google Scholar 

  2. D. E. Bell: A theorem concerning the integer lattice, Studies in Applied Math 56 (1977), 187–188.

    Google Scholar 

  3. J-P. Doignon: Convexity in Cristallographic lattices, J. of Geometry 3 (1973), 77–85.

    Google Scholar 

  4. L. Lovász: Geometry of numbers and integer programming in mathematical programming: Recent developments and applications, M. Iri and K. Tanabe (eds.), Kluwer, 1989, 177–210.

    Google Scholar 

  5. H. E. Scarf: Production sets with indivisibilities. Part I. Generalities, Econometrica 49 (1981), 1–32.

    Google Scholar 

  6. P. White: Discrete activity analysis, Ph.D Thesis, Yale University, Department of Economics, 1983.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Mathematical Institute, POB 127, 1364, Budapest, Hungary

    I. Bárány

  2. Cowles Foundation, Yale University, 06520, New Haven, CT

    H. E. Scarf

  3. Bellcore, 445 South Street, 07962, Morristown, NJ

    D. Shallcross

Authors
  1. I. Bárány
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  2. H. E. Scarf
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  3. D. Shallcross
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Editor information

Egon Balas Jens Clausen

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© 1995 Springer-Verlag Berlin Heidelberg

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Bárány, I., Scarf, H.E., Shallcross, D. (1995). The topological structure of maximal lattice free convex bodies: The general case. In: Balas, E., Clausen, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1995. Lecture Notes in Computer Science, vol 920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59408-6_55

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  • DOI: https://doi.org/10.1007/3-540-59408-6_55

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59408-6

  • Online ISBN: 978-3-540-49245-0

  • eBook Packages: Springer Book Archive

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