18 citations · 41 across the 13 of their papers we have counts for
Showing 2016 · math.MGShow all
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math.MG2016★ 1 cited
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…
math.MG2016★ 2 cited
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…
math.MG2016★ 1 cited
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…