IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1087.html
   My bibliography  Save this paper

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

Author

Listed:

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

Suggested Citation

  • Imre Barany & Herbert E. Scarf & David F. Shallcross, 1994. "The Topological Structure of Maximal Lattice Free Convex Bodies: The General Case," Cowles Foundation Discussion Papers 1087, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1087
    Note: CFP 959.
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d10/d1087.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Herbert E. Scarf, 2008. "Production Sets with Indivisibilities Part I: Generalities," Palgrave Macmillan Books, in: Zaifu Yang (ed.), Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research, chapter 2, pages 7-38, Palgrave Macmillan.
    3. Herbert E. Scarf, 2008. "Production Sets with Indivisibilities Part II. The Case of Two Activities," Palgrave Macmillan Books, in: Zaifu Yang (ed.), Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research, chapter 3, pages 39-67, Palgrave Macmillan.
    4. Herbert E. Scarf, 2008. "An observation on the structure of production sets with indivisibilities," Palgrave Macmillan Books, in: Zaifu Yang (ed.), Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research, chapter 1, pages 1-5, Palgrave Macmillan.
    5. Herbert E. Scarf & R. Kannan & Laszlo Lovasz, 1988. "The Shapes of Polyhedra," Cowles Foundation Discussion Papers 883, Cowles Foundation for Research in Economics, Yale University.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Herbert E. Scarf & Kevin M. Woods, 2008. "Neighborhood Complexes and Generating Functions for Affine Semigroups," Palgrave Macmillan Books, in: Zaifu Yang (ed.), Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research, chapter 12, pages 207-225, Palgrave Macmillan.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Robert Weismantel, 1998. "Test sets of integer programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(1), pages 1-37, February.
    2. Gerard van der Laan & Dolf Talman & Zaifu Yang, 2004. "Solving Discrete Zero Point Problems," Tinbergen Institute Discussion Papers 04-112/1, Tinbergen Institute.
    3. Kala Krishna & Cemile Yavas, 2004. "Lumpy consumer durables, market power, and endogenous business cycles," Canadian Journal of Economics, Canadian Economics Association, vol. 37(2), pages 375-391, May.
    4. Alberto Del Pia & Robert Hildebrand & Robert Weismantel & Kevin Zemmer, 2016. "Minimizing Cubic and Homogeneous Polynomials over Integers in the Plane," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 511-530, May.
    5. Cesaroni, Giovanni & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2017. "Global and local scale characteristics in convex and nonconvex nonparametric technologies: A first empirical exploration," European Journal of Operational Research, Elsevier, vol. 259(2), pages 576-586.
    6. Truchon, Michel, 1988. "Programmation mathématique et théorie économique," L'Actualité Economique, Société Canadienne de Science Economique, vol. 64(2), pages 143-156, juin.
    7. Kumaraswamy Velupillai, 2003. "Economics and the complexity vision: chimerical partners or elysian adventurers," Department of Economics Working Papers 0307, Department of Economics, University of Trento, Italia.
    8. Yang, Z.F., 1994. "A simplicial algorithm for testing the integral properties of polytopes : A revision," Other publications TiSEM 72b67872-ca37-4bb5-8a13-7, Tilburg University, School of Economics and Management.
    9. Walter Briec & Kristiaan Kerstens, 2006. "Input, output and graph technical efficiency measures on non-convex FDH models with various scaling laws: An integrated approach based upon implicit enumeration algorithms," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 135-166, June.
    10. Yang, Z.F., 1994. "A simplicial algorithm for testing the integral property of a polytope," Discussion Paper 1994-75, Tilburg University, Center for Economic Research.
    11. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 1999. "Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible, Indivisible Commodities and Linear Production Technologies," Other publications TiSEM e7e05539-3fab-4998-818d-0, Tilburg University, School of Economics and Management.
    12. Koshevoy, Gleb A. & Talman, Dolf, 2006. "Competitive equilibria in economies with multiple indivisible and multiple divisible commodities," Journal of Mathematical Economics, Elsevier, vol. 42(2), pages 216-226, April.
    13. Bruno Coquet & Jacques Le Cacheux, 1996. "Les privatisations dans la perspective de l'intégration européenne," Revue Économique, Programme National Persée, vol. 47(6), pages 1333-1350.
    14. Jensen Christian, 2014. "Replication and Returns to Scale in Production," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 14(1), pages 127-148, February.
    15. Rabia Nessah & Kristiaan Kerstens, 2008. "Characterizations of the Existence of Nash Equilibria with Non-convex Strategy Sets," Working Papers 2008-ECO-13, IESEG School of Management.
    16. Bennett Levitan & Jose Lobo & Stuart Kauffman & Richard Schuler, 1999. "Optimal Organization Size in a Stochastic Environment with Externalities," Working Papers 99-04-024, Santa Fe Institute.
    17. Koshevoy, G.A. & Talman, A.J.J., 2006. "Competitive Equilibria in Economies with Multiple Divisible and Indivisible Commodities and No Money," Other publications TiSEM 130306fe-6e3c-499c-b776-c, Tilburg University, School of Economics and Management.
    18. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2002. "Existence and welfare properties of equilibrium in an exchange economy with multiple divisible and indivisible commodities and linear production," Other publications TiSEM 5a5610bf-4f85-4a25-963c-c, Tilburg University, School of Economics and Management.
    19. Bennett Levitan & José Lobo & Richard Schuler & Stuart Kauffman, 2002. "Evolution of Organizational Performance and Stability in a Stochastic Environment," Computational and Mathematical Organization Theory, Springer, vol. 8(4), pages 281-313, December.
    20. C. Dang, 2001. "Computing an Integer Point of a Class of Convex Sets," Journal of Optimization Theory and Applications, Springer, vol. 108(2), pages 333-348, February.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:1087. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.