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The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg
Published 16 Jun 2017 in math.CO, cs.DM, and math.OC | (1706.05975v3)
Abstract: We discuss five discrete results: the lemmas of Sperner and Tucker from combinatorial topology and the theorems of Carath\'eodory, Helly, and Tverberg from combinatorial geometry. We explore their connections and emphasize their broad impact in application areas such as game theory, graph theory, mathematical optimization, computational geometry, etc.
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