2016/04/08 by Beauttie Kuture, Oscar Leong, Kuture, Beauttie +7
Mathematics · Social Sciences · #05A99 (Primary) 55M20 (Secondary) #Algebraic Topology (math.AT) #Cognitive and developmental aspects of mathematical skills #Combinatorics (math.CO) #FOS: Mathematics #Mathematics Education and Teaching Techniques #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.1604.02395
openalex publication_date 2016/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Sperner's lemma is a statement about labeled triangulations of a simplex. McLennan and Tourky (2007) provided a novel proof of Sperner's Lemma by examining volumes of simplices in a triangulation under time-linear simplex-linear deformation. We adapt a similar argument to prove Tucker's Lemma on a triangulated cross-polytope P. The McLennan-Tourky technique does not directly apply because this deformation may distort the volume of P. We remedy this by inscribing P in its dual polytope, triangulating it, and considering how the volumes of deformed simplices behave.