18 citations · 41 across the 13 of their papers we have counts for
17 papers
Discrepancy theory, Tverberg's theorem, and regression depth
Aleksey Lopez, Pablo Soberón
We prove new bounds for Tverberg's theorem with tolerance. We show that , where is the smallest number such that any set of points in $\math…
Tverberg partitions as weak epsilon-nets
Pablo Soberón
We prove a Tverberg-type theorem using the probabilistic method. Given , we find the smallest number of partitions of a set in into parts needed in or…
Robust Tverberg and colorful Carathéodory results via random choice
Pablo Soberón
We use the probabilistic method to obtain versions of the colorful Carathéodory theorem and Tverberg's theorem with tolerance. In particular, we give bounds for the smallest intege…
Quantitative Tverberg theorems over lattices and other discrete sets
J. A. De Loera, R. N. La Haye, D. Rolnick +1
This paper presents a new variation of Tverberg's theorem. Given a discrete set of , we study the number of points of needed to guarantee the existence of an -parti…
Quantitative combinatorial geometry for continuous parameters
J. A. De Loera, R. N. La Haye, D. Rolnick +1
We prove variations of Carathéodory's, Helly's and Tverberg's theorems where the sets involved are measured according to continuous functions such as the volume or diameter. Among…
Algorithms for Tverberg's theorem via centerpoint theorems
David Rolnick, Pablo Soberón
We obtain algorithms for computing Tverberg partitions based on centerpoint approximations. This applies to a wide range of convexity spaces, from the classic Euclidean setting to…