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Balanced Simplices on Polytopes
Eaves,C. van der Laan,G. Talman,A.J.J. Yang,Z.F.
Eaves,C.
van der Laan,G.
Talman,A.J.J.
Yang,Z.F.
Abstract
The 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.
Description
Pagination: 19
Date
1996
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Publisher
Operations research
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25.pdf
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Keywords
econometrics
Citation
Eaves, C, van der Laan, G, Talman, A J J & Yang, Z F 1996 'Balanced Simplices on Polytopes' CentER Discussion Paper, vol. 1996-25, Operations research, Tilburg.