Some new results on geometric transversals
From MaRDI portal
Publication:6624172
DOI10.1007/s00454-023-00573-2MaRDI QIDQ6624172
Andreas F. Holmsen, Otfried Schwarzkopf, Xavier Goaoc
Publication date: 25 October 2024
Published in: Discrete \& Computational Geometry (Search for Journal in Brave)
Helly-type theoremsgeometric transversal theoryapplication of the Borsuk-Ulam theoremspace of transversals
Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Helly-type theorems and geometric transversal theory (52A35)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A new topological Helly theorem and some transversal results
- Lower bounds for weak epsilon-nets and stair-convexity
- Topological transversals to a family of convex sets
- No Helly theorem for stabbing translates by lines in \(\mathbb{R}^3\)
- A topological colorful Helly theorem
- A generalization of Hadwiger's transversal theorem to intersecting sets
- Necessary and sufficient conditions for hyperplane transversals
- Über ein Problem aus der kombinatorischen Geometrie
- On common transversals
- Homotopy properties of greedoids
- A generalization of Caratheodory's theorem
- Piercing convex sets and the Hadwiger-Debrunner \((p,q)\)-problem
- Proof of Grünbaum's conjecture on common transversals for translates
- Separoids, their categories and a Hadwiger-type theorem for transversals
- The colored Hadwiger transversal theorem in \(\mathbb{R}^d\)
- Lower bounds to Helly numbers of line transversals to disjoint congruent balls
- Über Systeme von abgeschlossenen Mengen mit gemeinschaftlichen Punkten.
- Transversal numbers for hypergraphs arising in geometry
- Bounding the piercing number
- On the connected components of the space of line transversals to a family of convex sets
- Oriented matroids and hyperplane transversals
- Radon numbers and the fractional Helly theorem
- How do 9 points look like in \(\mathbb{E}^3\)?
- Further consequences of the colorful Helly hypothesis
- On weak \(\epsilon\)-nets and the Radon number
- A colorful theorem on transversal lines to plane convex sets
- Helly numbers of acyclic families
- Line transversals to disjoint balls
- Helly-type theorems for line transversals to disjoint unit balls
- Helly’s theorem: New variations and applications
- Common Transversals for Families of Sets†
- Hadwiger's Transversal Theorem In Higher Dimensions
- Point Selections and Weak ε-Nets for Convex Hulls
- Bounding Helly Numbers via Betti Numbers
- Oriented Matroids
- A conjecture of Grünbaum on common transversals.
- Foundations of a theory of convexity on affine Grassmann manifolds
- The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg
- Transversals, Topology and Colorful Geometric Results
- Cremona convexity, frame convexity and a theorem of Santaló
- Helly Type Theorems Derived From Basic Singular Homology
- Helly-type problems
- Using the Borsuk-Ulam theorem. Lectures on topological methods in combinatorics and geometry. Written in cooperation with Anders Björner and Günter M. Ziegler
- Stronger bounds for weak epsilon-nets in higher dimensions
This page was built for publication: Some new results on geometric transversals