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Algorithms to Find Completely-Labelled Simplices

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Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 124)

Abstract

While the proof of Sperner’s lemma given in 1.4 does not suggest any method to find completely-labelled simplices, we noted in example I.4.3 that n-simplices of G with the labels 0,1,...,n-1 formed paths. Cohen [6] gave a proof of Sperner’s lemma based on these paths; we present his argument in Section 1. Cohen’s proof is inductive—we still have the problem of how to start. Two possible methods will be given in Section 2. Sections 3 and 4 show how these methods can be implemented using K2 (m). Section 5 describes Scarf’s algorithm, and Section 6 illustrates the algorithms with an example.

Keywords

Simple Path Simple Circuit Barycentric Subdivision Approximate Fixed Point Variable Dimension Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  1. 1.School of Operations Research and Industrial EngineeringCornell UniversityIthacaUSA

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