ISSN:
1436-4646
Keywords:
Sperner's lemma
;
simplicial pivoting
;
fixed point algorithms
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract In a recent paper, Gale has given an interesting generalization of the KKM lemma in combinatorial topology. We present a similar generalization of Sperner's well-known lemma and give a constructive proof. The argument uses the familiar idea of following simplicial paths in a triangulation. To demonstrate that the algorithm must work, orientation considerations are necessary. Gale's generalized KKM lemma is derived from the main result. A permutation-based generalization of Brouwer's fixed point theorem is also given.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01587081
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