tverberg’s theorem
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2018 ◽  
Vol 55 (4) ◽  
pp. 459-492 ◽  
Author(s):  
Imre Bárány ◽  
Pablo Soberón
Keyword(s):  

2017 ◽  
Vol 27 (3) ◽  
pp. 427-440 ◽  
Author(s):  
PABLO SOBERÓN

We use the probabilistic method to obtain versions of the colourful Carathéodory theorem and Tverberg's theorem with tolerance.In particular, we give bounds for the smallest integer N = N(t,d,r) such that for any N points in ℝd, there is a partition of them into r parts for which the following condition holds: after removing any t points from the set, the convex hulls of what is left in each part intersect.We prove a bound N = rt + O($\sqrt{t}$) for fixed r,d which is polynomial in each parameters. Our bounds extend to colourful versions of Tverberg's theorem, as well as Reay-type variations of this theorem.


2016 ◽  
Vol 216 (2) ◽  
pp. 957-972 ◽  
Author(s):  
Micha A. Perles ◽  
Moriah Sigron
Keyword(s):  

2016 ◽  
Vol 63 (07) ◽  
pp. 732-739 ◽  
Author(s):  
Imre Bárány ◽  
Pavle V. M. Blagojević ◽  
Günter M. Ziegler
Keyword(s):  

2013 ◽  
Vol 51 (1) ◽  
pp. 207-220
Author(s):  
Alexander Engström ◽  
Patrik Norén

2012 ◽  
Vol 47 (3) ◽  
pp. 455-460 ◽  
Author(s):  
Pablo Soberón ◽  
Ricardo Strausz
Keyword(s):  

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