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

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	415-511
Number of pages	97
Journal	Bulletin of the American Mathematical Society
Volume	56
Issue number	3
DOIs	https://doi.org/10.1090/bull/1653
Publication status	Published - 1 Jan 2019

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

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