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.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1996-25.
Date of creation: 1996
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- 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.
- 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.
- C. B. Garcia, 1976. "A Hybrid Algorithm for the Computation of Fixed Points," Management Science, INFORMS, vol. 22(5), pages 606-613, January.
- 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.
- 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.
- 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.
- 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.
- 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.
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