Let F $\mathcal F $ https://s3-euw1-ap-pe-df-pch-content-public-p. s3. eu-west-1.
amazonaws. com/9781315119601/fb8178cb-c53c-4311-b072-eff5ec016aba/content/inline …

We initiate the study of no-dimensional versions of classical theorems in convexity. One
example is Carathéodory's theorem without dimension: given an n-element set P in a …

Let HD d (p, q) denote the minimal size of a transversal that can always be guaranteed for a
family of compact convex sets in Rd which satisfy the (p, q)-property (p≥ q≥ d+ 1). In a …

A Helly-type theorem for diameter provides a bound on the diameter of the intersection of a
finite family of convex sets in R^d given some information on the diameter of the intersection …

In this short paper, we show that if $\left\{\mathcal {F} _ {n}\right\} _ {n\in\mathbb {N}} $ be a
collection of families compact $(r, R) $-fat convex sets in $\mathbb {R}^{d} $ and if every …

The well known fractional Helly theorem and colorful Helly theorem can be merged into the
so called colorful fractional Helly theorem. It states: For every $\alpha\in (0, 1] $ and every …

Let HD d (p, q) denote the minimal size of a transversal that can always be guaranteed for a
family of compact convex sets in ℝ d which satisfy the (p, q)-property (p≥ q≥ d+ 1). In a …

arXiv:1508.07606v2 [math.MG] 8 Mar 2016 Page 1 Contemporary Mathematics Helly’s
Theorem: New Variations and Applications Nina Amenta, Jesús A. De Loera, and Pablo …

We show quantitative versions of classical 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 …

Helly's theorem is a classical result concerning the intersection patterns of convex sets in R
d. Two important generalizations are the colorful version and the fractional version …