A constructive proof of Ky Fan's generalization of Tucker's lemma

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:111

Article

Prescott, T ; Su, FE

关键词: Tucker's lemma;    Fan's lemma;    Borsuk-Ulam theorem;    Lusternik-Schnirelman-Borsuk theorem;    triangulations;   

DOI  :  10.1016/j.jcta.2004.12.005

来源: Elsevier

【 摘 要 】

We present a proof of Ky Fan's combinatorial lemma on labellings of triangulated spheres that differs from earlier proofs in that it is constructive. We slightly generalize the hypotheses of Fan's lemma to allow for triangulations of S-n that contain a flag of hemispheres. As a consequence, we can obtain a constructive proof of Tucker's lemma that holds for a more general class of triangulations than the usual version. (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

Free