The discrete yet ubiquitous theorems of Caratheodory, Helly, Sperner, Tucker, and Tverberg

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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https://hal.inria.fr/hal-02050466
Contributor : Xavier Goaoc <>
Submitted on : Wednesday, February 27, 2019 - 10:58:24 AM
Last modification on : Wednesday, August 7, 2019 - 12:19:20 PM

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Jesús A. de Loera, Xavier Goaoc, Frédéric Meunier, Nabil Mustafa. The discrete yet ubiquitous theorems of Caratheodory, Helly, Sperner, Tucker, and Tverberg. Bulletin of the American Mathematical Society, American Mathematical Society, In press, ⟨10.1090/bull/1653⟩. ⟨hal-02050466⟩

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