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

Jesús A. De Loera; Xavier Goaoc; Frédéric Meunier; Nabil H. Mustafa

doi:10.1090/bull/1653

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

Jesús A. De Loera
, Xavier Goaoc
, Frédéric Meunier
, Nabil H. Mustafa

University of California, Davis
Nancy Université
Université Paris-Est

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We discuss five fundamental results of discrete mathematics: the lemmas of Sperner and Tucker from combinatorial topology and the theorems of Carathéodory, Helly, and Tverberg from combinatorial geometry. We explore their connections and emphasize their broad impact in application areas such as data science, game theory, graph theory, mathematical optimization, computational geometry, etc.

langue originale	Anglais
Pages (de - à)	415-511
Nombre de pages	97
journal	Bulletin of the American Mathematical Society
Volume	56
Numéro de publication	3
Les DOIs	https://doi.org/10.1090/bull/1653
état	Publié - 1 janv. 2019

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10.1090/bull/1653

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title = "The discrete yet ubiquitous theorems of Carath{\'e}odory, Helly, Sperner, Tucker, and Tverberg",

abstract = "We discuss five fundamental results of discrete mathematics: the lemmas of Sperner and Tucker from combinatorial topology and the theorems of Carath{\'e}odory, Helly, and Tverberg from combinatorial geometry. We explore their connections and emphasize their broad impact in application areas such as data science, game theory, graph theory, mathematical optimization, computational geometry, etc.",

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AB - We discuss five fundamental results of discrete mathematics: the lemmas of Sperner and Tucker from combinatorial topology and the theorems of Carathéodory, Helly, and Tverberg from combinatorial geometry. We explore their connections and emphasize their broad impact in application areas such as data science, game theory, graph theory, mathematical optimization, computational geometry, etc.

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

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