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.
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© 1976 Springer-Verlag Berlin Heidelberg
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Todd, M.J. (1976). Algorithms to Find Completely-Labelled Simplices. In: The Computation of Fixed Points and Applications. Lecture Notes in Economics and Mathematical Systems, vol 124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-50327-6_4
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DOI: https://doi.org/10.1007/978-3-642-50327-6_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-07685-8
Online ISBN: 978-3-642-50327-6
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