2003•arXiv (Cornell University)Open access

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

Timothy Prescott, Francis Edward Su

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.

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Key concepts: Constructive, Constructive proof, Lemma (botany), Mathematical proof, Mathematics, Generalization, Combinatorial proof, Combinatorics