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- Marek Eliáš, Jirí Matousek, Edgardo Roldán-Pensado, Zuzana Safernová
- SIAM J. Discrete Math.
- 2014

We continue a sequence of recent works studying Ramsey functions for semialgebraic predicates in $\mathbb{R}^d$. A $k$-ary semialgebraic predicate $\Phi(x_1,\ldots,x_k)$ on $\mathbb{R}^d$ is a… (More)

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)

- Jesús Jerónimo-Castro, Edgardo Roldán-Pensado
- Discrete & Computational Geometry
- 2011

Let K be a convex body in the plane. Define λ(K,t) as the smallest number satisfying the following: if $\mathcal{F}$ is any family of translates of K such that every t members of $\mathcal{F}$ have a… (More)

Let $$\mathcal {F}$$F be a family of convex sets in $${\mathbb {R}}^d,$$Rd, which are colored with $$d+1$$d+1 colors. We say that $$\mathcal {F}$$F satisfies the Colorful Helly Property if every… (More)

- Edgardo Roldán-Pensado, Pablo Soberón
- Discrete & Computational Geometry
- 2014

In this paper we study Nd(k), the smallest positive integer such that any nice measure μ in $\mathbb{R}^{d}$ can be partitioned into Nd(k) convex parts of equal measure so that every hyperplane… (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)

- Jorge L. Arocha, Jesús Jerónimo-Castro, Luis Pedro Montejano, Edgardo Roldán-Pensado
- Periodica Mathematica Hungarica
- 2010

In this paper the following is proved: letK ∈ ℝ2be a convex body and t ∈ [0, 1/4]. If the diameter of K is at least √37 times the minimum width, then there is a pair of orthogonal lines that… (More)

In a Hilbert space H, the n-rank numerical range of a bounded linear operator T:H→ H is defined as the set of such that there exists a projection P of rank n that satisfies PTP=λ P. This is a… (More)