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

Abstract

We present a constructive proof of Ky Fan's combinatorial lemma concerning labellings of triangulated spheres. Our construction works for triangulations of $S^n$ that contain a flag of hemispheres. As a consequence, we produce a constructive proof of Tucker's lemma that holds for a larger class of triangulations than previous constructive proofs.

related work at http://www.math.hmc.edu/~su/papers.html

Cited by in corpus (1)

• The Borsuk-Ulam-property, Tucker-property and constructive proofs in combinatorics