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We study S-convex sets, which are the geometric objects obtained as the intersection of the usual convex sets in R with a proper subset S ⊂ R. We contribute new results about their S-Helly numbers.… (More)

We present Helly-type theorems where the convex sets are required to intersect a subset S of R d . This is a continuation of prior work for S = R d , Z d , and Z d k R k (motivated by mixed-integer… (More)

This paper presents sixteen quantitative versions of the classic Tverberg, Helly, & Caratheodory theorems in combinatorial convexity. Our results include measurable or enumerable information in the… (More)

- Jesús A. De Loera, Reuben N. La Haye, David Rolnick, Pablo Soberón
- Discrete & Computational Geometry
- 2016

This paper presents a new variation of Tverberg’s theorem. Given a discrete set S of $$\mathbb {R}^{d}$$Rd, we study the number of points of S needed to guarantee the existence of an m-partition of… (More)

- Jesús A. De Loera, Reuben N. La Haye, David Rolnick, Pablo Soberón
- Discrete & Computational Geometry
- 2016

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 our results, we… (More)

The scenario approach developed by Calafiore and Campi to attack chance-constrained
convex programs utilizes random sampling on the uncertainty parameter to substitute the
original problem with a… (More)

In this senior thesis, we study many different properties of symmetric point sets, focusing on points with only prime coordinates. The ultimate goal of this project is to find the Helly number of… (More)

Author(s): De Loera, J. A.; La Haye, R. N.; Oliveros, D.; Roldan-Pensado, E. | Abstract: We study $S$-convex sets, which are the geometric objects obtained as the intersection of the usual convex… (More)

- Jesús A. De Loera, Reuben N. La Haye, Amanda Montejano, Deborah Oliveros, Edgardo Roldán-Pensado
- Discrete Mathematics
- 2014

We present a Rainbow Ramsey version of the well-known Ramsey-type theorem of Richard Rado. We use new techniques from the Geometry of Numbers. We also disprove two conjectures proposed in the… (More)