TVERBERG'S THEOREM IS 50 YEARS OLD: A SURVEY

被引：35
作者：
Barany, Imre [1 ,2 ]
Soberon, Pablo [3 ]
机构：
[1] Hungarian Acad Sci, Alfred Renyi Inst Math, Pf 127, H-1364 Budapest, Hungary
[2] UCL, Dept Math, Gower St, London WC1E 6BT, England
[3] Northeastern Univ, Dept Math, Boston, MA 02115 USA
来源：
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 55卷 / 04期
基金：
美国国家科学基金会;
关键词：
TOPOLOGICAL GENERALIZATION; OPTIMAL BOUNDS; NUMBER; POINTS; PARTITIONS; CONJECTURE; SETS; INTERSECTION; COMPLEXITY; EXTENSION;
D O I：
10.1090/bull/1634
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This survey presents an overview of the advances around Tverberg's theorem, focusing on the last two decades. We discuss the topological, linear-algebraic, and combinatorial aspects of Tverberg's theorem and its applications. The survey contains several open problems and conjectures.
引用
收藏
页码：459 / 492
页数：34
相关论文
共 129 条
[1]  
Alfonsín JLR, 2001, EUR J COMBIN, V22, P723
[2]   THE CHROMATIC NUMBER OF KNESER HYPERGRAPHS [J].
ALON, N ;
FRANKL, P ;
LOVASZ, L .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 298 (01) :359-370
[3]   PIERCING CONVEX-SETS AND THE HADWIGER-DEBRUNNER (P, Q)-PROBLEM [J].
ALON, N ;
KLEITMAN, DJ .
ADVANCES IN MATHEMATICS, 1992, 96 (01) :103-112
[4]   Helly's theorem: New variations and applications [J].
Amenta, Nina ;
De Loera, Jesus A. ;
Soberon, Pablo .
ALGEBRAIC AND GEOMETRIC METHODS IN DISCRETE MATHEMATICS, 2017, 685 :55-95
[5]  
[Anonymous], 2018, ARXIV180507197
[6]  
[Anonymous], 2016, Notices of the American Mathematical Society, DOI 10.1090/noti1415
[7]  
[Anonymous], 1972, Bull. Lond. Math. Soc.
[8]  
[Anonymous], 2015, ARXIV150802349
[9]  
[Anonymous], 2015, Oberwolfach Reports
[10]   Transversals to the convex hulls of all k-sets of discrete subsets of Rn [J].
Arocha, J. L. ;
Bracho, J. ;
Montejano, L. ;
Alfonsin, J. L. Ramirez .
JOURNAL OF COMBINATORIAL THEORY SERIES A, 2011, 118 (01) :197-207
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