Helly-type problems-Reference-Cited by-同舟云学术

Helly-type problems

Published:2021-10-29 Issue:4 Volume:59 Page:471-502
ISSN:0273-0979
Container-title:Bulletin of the American Mathematical Society
language:en
Short-container-title:Bull. Amer. Math. Soc.

Author:

Bárány Imre,Kalai Gil

Abstract

In this paper we present a variety of problems in the interface between combinatorics and geometry around the theorems of Helly, Radon, Carathéodory, and Tverberg. Through these problems we describe the fascinating area of Helly-type theorems and explain some of their main themes and goals.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/bull/2022-59-04/S0273-0979-2021-01753-8/S0273-0979-2021-01753-8.pdf

Reference129 articles.

1. The intersection of a matroid and a simplicial complex;Aharoni, Ron;Trans. Amer. Math. Soc.,2006

2. Rainbow matchings in 𝑟-partite 𝑟-graphs;Aharoni, Ron;Electron. J. Combin.,2009

3. Quantitative Helly-type theorems via sparse approximation;Almendra-Hernández, V. H.,2021

4. Point selections and weak 𝜀-nets for convex hulls;Alon, Noga;Combin. Probab. Comput.,1992

5. Bounding the piercing number;Alon, N.;Discrete Comput. Geom.,1995

Cited by 8 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Positive bases, cones, Helly-type theorems;Mathematica Slovaca;2024-06-01

2. Some New Results on Geometric Transversals;Discrete & Computational Geometry;2023-11-16

3. Convexity in (Colored) Affine Semigroups;Studia Scientiarum Mathematicarum Hungarica;2023-10-24

4. Combinatorial properties of nonarchimedean convex sets;Pacific Journal of Mathematics;2023-05-29

5. Convex Sets;Texts and Readings in Mathematics;2023