Balanced Simplices on Polytopes
AbstractThe well known Sperner lemma states that in a simplicial subdivision of a simplex with a properly labeled boundary there is a completely labeled simplex. We present two combinatorial theorems on polytopes which generalize Sperner's lemma.Using balanced simplices, a generalized concept of completely labeled simplices, a uni ed existence result of balanced simplices in any simplicial subdivision of a polytope is given.This theorem implies the well-known lemmas of Sperner, Scarf, Shapley, and Garcia as well as some other results as special cases.A second theorem which imposes no restrictions on the integer labeling rule is established; this theorem implies several results of Freund.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1996-25.
Date of creation: 1996
Date of revision:
Contact details of provider:
Web page: http://center.uvt.nl
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- C. B. Garcia, 1976. "A Hybrid Algorithm for the Computation of Fixed Points," Management Science, INFORMS, vol. 22(5), pages 606-613, January.
- Freund, Robert Michael., 1985. "Combinatorial analogs of Brouwer's fixed point theorem on a bounded polyhedron," Working papers 1720-85., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Talman, A.J.J. & Laan , G. van der, 1982. "On the computation of fixed points on the product space of unit simplices and an application to noncooperative N-person games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153028, Tilburg University.
- Herbert E. Scarf, 1967. "The Approximation of Fixed Points of a Continuous Mapping," Cowles Foundation Discussion Papers 216R, Cowles Foundation for Research in Economics, Yale University.
- Talman, A.J.J. & Laan, G. van der & Van der Heyden, L., 1987. "Variable dimension algorithms for solving the nonlinear complementarity problem on a product of unit simplices using general labelling," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153106, Tilburg University.
- Talman, A.J.J. & Laan, G. van der, 1979. "A restart algorithm for computing fixed points without an extra dimension," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153012, Tilburg University.
- Laan, G. van der & Talman, A.J.J. & Yang, Z.F., 2010. "Combinatorial integer labeling theorems on finite sets with applications," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3764045, Tilburg University.
- Laan, G. van der & Talman, A.J.J. & Yang, Z.F., 2007.
"Combinatorial Integer Labeling Thorems on Finite Sets with an Application to Discrete Systems of Nonlinear Equations,"
2007-88, Tilburg University, Center for Economic Research.
- Gerard van der Laan & Dolf Talman & Zaifu Yang, 2007. "Combinatorial Integer Labeling Theorems on Finite Sets with an Application to Discrete Systems of Nonlinear Equations," Tinbergen Institute Discussion Papers 07-084/1, Tinbergen Institute.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Richard Broekman).
If references are entirely missing, you can add them using this form.