A Constructive Proof of Ky Fan's Generalization of Tucker's Lemma

Authors

Timothy Prescott '02, Harvey Mudd CollegeFollow
Francis E. Su, Harvey Mudd CollegeFollow

Student Co-author

HMC Undergraduate

Document Type

Article - preprint

Department

Mathematics (HMC)

Publication Date

8-2005

Abstract

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 Sⁿ 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.

Comments

Author's pre-print manuscript available for download.

For the publisher's version, please visit http://dx.doi.org/10.1016/j.jcta.2004.12.005.

Rights Information

© 2005 Elsevier

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1016/j.jcta.2004.12.005

Recommended Citation

Timothy Prescott and Francis Edward Su. A constructive proof of Ky Fan's generalization of Tucker's lemma. J. Combin. Theory Ser. A, 111(2):257–265, 2005.