The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg
Jesús A. De Loera, Xavier Goaoc, Frédéric Meunier, Nabil H. Mustafa · Bulletin of the American Mathematical Society · 2019
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.