9 papers
-vector fans and picture categories for 0-Auslander extriangulated categories
Erlend D. Børve, Maximilian Kaipel
We extend the notion of -vector fan so that it is defined for a Hom-finite Krull-Schmidt 0-Auslander -linear extriangulated category with a projective…
A Colorful Extension of VC-dimension and Geometric Applications
Chaya Keller, Shakhar Smorodinsky
The VC-dimension is a fundamental measure of the complexity of a set system. In this paper, we introduce and study a colorful variant of VC-dimension that captures the behavior of…
New Sufficient Conditions for Linear-Sized Epsilon-Nets and -Theorems
Chaya Keller, Shakhar Smorodinsky
An -net theorem for a hypergraph upper bounds the minimum size of a vertex set that pierces all -heavy hyperedges. A -theorem bounds from above the minimum size of a…
On the Largest Convexity Number of Co-Finite Sets in the Plane
Chaya Keller, Micha A. Perles
The convexity number of a set is the minimum number of convex subsets required to cover it. We study the following question: what is the largest possible c…
Error Resilient Space Partitioning
Orr Dunkelman, Zeev Geyzel, Chaya Keller +4
A major research area in discrete geometry is to consider the best way to partition the -dimensional Euclidean space under various quality criteria. In this paper…
An -Theorem for -Transversals
Chaya Keller, Micha A. Perles
A family of sets satisfies the -property if among every members of , some can be pierced by a single point. The celebrated -theorem…