Theorems of Carathéodory, Helly, and Tverberg without dimension
Karim Adiprasito, Imre Bárány, Nabil H. Mustafa · Society for Industrial and Applied Mathematics eBooks · 2019
Motivated by Barman [6], we initiate a systematic study of the ‘no-dimensional’ analogues of some basic theorems in combinatorial and convex geometry, including the colorful Carathéodory's theorem, Tverberg's theorem, Helly's theorem as well as their fractional and colorful extensions.