The discrete yet ubiquitous theorems of Caratheodory, Helly, Sperner, Tucker, and Tverberg - Archive ouverte HAL Access content directly
Journal Articles Bulletin of the American Mathematical Society Year : 2019

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

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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.

Dates and versions

hal-02050466 , version 1 (27-02-2019)

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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, 2019, 56, pp.415-511. ⟨10.1090/bull/1653⟩. ⟨hal-02050466⟩
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