Tverberg’s theorem is 50 years old: A survey
From MaRDI portal
Publication:4684365
DOI10.1090/bull/1634zbMath1401.52012arXiv1712.06119OpenAlexW2963327863WikidataQ129577704 ScholiaQ129577704MaRDI QIDQ4684365
Publication date: 28 September 2018
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1712.06119
History of mathematics in the 20th century (01A60) History of convex and discrete geometry (52-03) Other problems of combinatorial convexity (52A37) Helly-type theorems and geometric transversal theory (52A35) Research exposition (monographs, survey articles) pertaining to convex and discrete geometry (52-02)
Related Items
Stochastic Tverberg Theorems With Applications in Multiclass Logistic Regression, Separability, and Centerpoints of Data, Tverberg's theorem, disks, and Hamiltonian cycles, Eliminating higher-multiplicity intersections. III. Codimension 2, Tolerance for colorful Tverberg partitions, A survey of mass partitions, The coloured Tverberg theorem, extensions and new results, Tverberg-type theorems with altered intersection patterns (nerves), Radon numbers grow linearly, Topological drawings meet classical theorems from convex geometry, Inscribed Tverberg‐type partitions for orbit polytopes, Matching points with disks with a common intersection, Tverberg's theorem for cell complexes, New lower bounds for Tverberg partitions with tolerance in the plane, Support vector machines and Radon's theorem, Plus minus analogues for affine Tverberg type results, Neighboring mapping points theorem, An application of the universality theorem for Tverberg partitions to data depth and hitting convex sets, Regular polygonal partitions of a Tverberg type, Algorithms for Radon partitions with tolerance, Radon numbers and the fractional Helly theorem, Strong independence and the dimension of a Tverberg set, Quantitative combinatorial geometry for concave functions, Continuous maps with the disjoint support property, The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg, Tverberg theorems over discrete sets of points, No‐dimension Tverberg's theorem and its corollaries in Banach spaces of type p, Multi-colored spanning graphs, Counterexamples to the colorful Tverberg conjecture for hyperplanes, Topological Drawings Meet Classical Theorems from Convex Geometry
Cites Work
- A Generalization of Radon's Theorem
- On Sets Projectively Equivalent to the Vertices of a Convex Polytope
- Classifying unavoidable Tverberg partitions
- Approximating Tverberg points in linear time for any fixed dimension
- 10 points in dimension 4 not projectively equivalent to the vertices of a convex polytope
- Lawrence oriented matroids and a problem of McMullen on projective equivalences of polytopes
- Partitions of points into simplices with \(k\)-dimensional intersection. II: Proof of Reay's conjecture in dimensions 4 and 5
- A combinatorial mathematician in Norway: Some personal reflections
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Complete Kneser transversals
- On the number of colored Birch and Tverberg partitions
- A simpler proof of the Boros-Füredi-Bárány-Pach-Gromov theorem
- A generalisation of Tverberg's theorem
- Average-value Tverberg partitions via finite Fourier analysis
- Some variations on Tverberg's theorem
- Quantitative combinatorial geometry for continuous parameters
- Equal coefficients and tolerance in coloured Tverberg partitions
- Positive-fraction intersection results and variations of weak epsilon-nets
- Lower bounds for weak epsilon-nets and stair-convexity
- Transversals to the convex hulls of all \(k\)-sets of discrete subsets of \(\mathbb R^n\)
- Tverberg-type theorems for intersecting by rays
- Optimal bounds for a colorful Tverberg-Vrećica type problem
- A topological colorful Helly theorem
- Singularities, expanders and topology of maps. II: From combinatorics to topology via algebraic isoperimetry
- A generalized Kneser conjecture
- Kneser's conjecture, chromatic number, and homotopy
- Supersaturated graphs and hypergraphs
- Stabbing simplices by points and flats
- On the number of Tverberg partitions in the prime power case
- The intersection of a matroid and an oriented matroid
- Tverberg's theorem with constraints
- Approximate centerpoints with proofs
- On the number of Birch partitions
- New cases of Reay's conjecture on partitions of points into simplices with \(k\)-dimensional intersection
- The number of triangles covering the center of an \(n\)-set
- A certain combinatorial inequality
- Several generalizations of Tverberg's theorem
- Partition numbers for trees and ordered sets
- A generalization of Caratheodory's theorem
- The colored Tverberg's problem and complexes of injective functions
- A generalization of the ham sandwich theorem
- Piercing convex sets and the Hadwiger-Debrunner \((p,q)\)-problem
- On generalizations of Radon's theorem and the Ham sandwich theorem
- Depth in an arrangement of hyperplanes
- On a topological generalization of the Tverberg theorem
- A Tverberg-type result on multicolored simplices
- Tverberg's conjecture
- The Radon number of the three-dimensional integer lattice
- The partition conjecture
- On Reay's relaxed Tverberg conjecture and generalizations of Conway's thrackle conjecture
- An improvement on the Rado bound for the centerline depth
- Note on a conjecture of Sierksma
- Tverberg's theorem via number fields
- The Tverberg-Vrećica problem and the combinatorial geometry on vector bundles
- Orthogonal representations and connectivity of graphs
- Tverberg plus minus
- Barycenters of polytope skeleta and counterexamples to the topological Tverberg conjecture, via constraints
- Quantitative \((p, q)\) theorems in combinatorial geometry
- Eliminating higher-multiplicity intersections. III. Codimension 2
- Tverberg partitions as weak epsilon-nets
- Optimal bounds for the colored Tverberg problem
- Carathéodory, Helly and the others in the max-plus world
- Very colorful theorems
- Helge Tverberg is eighty: a personal tribute
- Quantitative Tverberg theorems over lattices and other discrete sets
- A note on the Tolerant Tverberg Theorem
- Tverberg's transversal conjecture and analogues of nonembeddability theorems for transversals
- An extension of Radon's theorem
- A theorem on families of sets
- Convexity in cristallographical lattices
- On Tverberg partitions
- On the number of halving planes
- The self-intersections of a smooth \(n\)-manifold in \(2n\)-space
- Tverberg plus constraints
- Tverberg's Theorem at 50: Extensions and Counterexamples
- Helly’s theorem: New variations and applications
- Intersection patterns of finite sets and of convex sets
- Helly-type theorems for the diameter
- A Generalized van Kampen-Flores Theorem
- An Extension of the Ham Sandwich Theorem
- Dual theorems on central points and their generalizations
- Simple proofs of some Borsuk-Ulam results
- The Chromatic Number of Kneser Hypergraphs
- On a common generalization of Borsuk's and Radon's theorem
- On a Topological Generalization of a Theorem of Tverberg
- A generalization of Radon's theorem II
- On the Geometry and Computational Complexity of Radon Partitions in the Iinteger Lattice
- Equivariant Cohomology and Lower Bounds for Chromatic Numbers
- A Colored Version of Tverberg's Theorem
- An observation on the structure of production sets with indivisibilities
- A Theorem Concerning the Integer Lattice
- The m-core properly contains the m-divisible points in space
- Point Selections and Weak ε-Nets for Convex Hulls
- Colourful Linear Programming and its Relatives
- Convex Polytopes
- Theory of Quantum Error Correction for General Noise
- A Tverberg type theorem for matroids
- Beyond the Borsuk–Ulam Theorem: The Topological Tverberg Story
- One-Sided Epsilon-Approximants
- Robust Tverberg and Colourful Carathéodory Results via Random Choice
- The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg
- ALGORITHMS FOR TOLERANT TVERBERG PARTITIONS
