14 citations · 35 across the 7 of their papers we have counts for
7 papers
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…
On the robust hardness of Gröbner basis computation
Gwen Spencer, David Rolnick
The computation of Gröbner bases is an established hard problem. By contrast with many other problems, however, there has been little investigation of whether this hardness is robu…
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…
Quantitative theorems in combinatorial geometry
David Rolnick, Pablo Soberón
We show quantitative versions of classic results in discrete geometry, where the size of a convex set is determined by some non-negative function. We give versions of this kind for…