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

2005/07/13 by Mark de Longueville, de Longueville, Mark, Rade T. Živaljević +2 · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology #Topological and Geometric Data Analysis #math.CO #msc:05-xx #msc:52-xx

paper · pdf · doi:10.48550/arxiv.math/0507269

12 pages, 0 figures

arxiv created 2005/07/13 · arxiv updated 2009/12/01

Abstract

This article is concerned with a general scheme on how to obtain constructive proofs for combinatorial theorems that have topological proofs so far. To this end the combinatorial concept of Tucker-property of a finite group G is introduced and its relation to the topological Borsuk-Ulam-property is discussed. Applications of the Tucker-property in combinatorics are demonstrated.

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