14 citations · 14 across the 1 of their papers we have counts for
3 papers
math.MG2016
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
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…
math.MG2015★ 14 cited
Quantitative Tverberg, Helly, & Carathéodory theorems
J. A. De Loera, R. N. La Haye, D. Rolnick +1
This paper presents sixteen quantitative versions of the classic Tverberg, Helly, & Caratheodory theorems in combinatorial convexity. Our results include measurable or enumerable i…