Multifractal Analysis of Chaotic Point Sets

1992 ◽  
Author(s):  
L. V. Meisel ◽  
M. A. Johnson
2003 ◽  
Vol 40 (3) ◽  
pp. 269-286 ◽  
Author(s):  
H. Nyklová

In this paper we study a problem related to the classical Erdos--Szekeres Theorem on finding points in convex position in planar point sets. We study for which n and k there exists a number h(n,k) such that in every planar point set X of size h(n,k) or larger, no three points on a line, we can find n points forming a vertex set of a convex n-gon with at most k points of X in its interior. Recall that h(n,0) does not exist for n = 7 by a result of Horton. In this paper we prove the following results. First, using Horton's construction with no empty 7-gon we obtain that h(n,k) does not exist for k = 2(n+6)/4-n-3. Then we give some exact results for convex hexagons: every point set containing a convex hexagon contains a convex hexagon with at most seven points inside it, and any such set of at least 19 points contains a convex hexagon with at most five points inside it.


2018 ◽  
Vol 14 (1) ◽  
pp. 51-60
Author(s):  
Emilian DANILA ◽  
VALENTIN Hahuie ◽  
Puiu Lucian GEORGESCU ◽  
Luminița MORARU

2010 ◽  
Vol 36 (8) ◽  
pp. 1073-1083 ◽  
Author(s):  
Xu-Fang PANG ◽  
Ming-Yong PANG ◽  
Chun-Xia XIAO
Keyword(s):  

1986 ◽  
Vol 12 (1) ◽  
pp. 377 ◽  
Author(s):  
Morgan
Keyword(s):  

2021 ◽  
Vol 31 (3) ◽  
pp. 033110
Author(s):  
Samuel Toluwalope Ogunjo ◽  
Ibiyinka Fuwape ◽  
A. Babatunde Rabiu ◽  
Sunday Samuel Oluyamo

2019 ◽  
Vol 15 (3) ◽  
pp. 1-16
Author(s):  
Avrim Blum ◽  
Sariel Har-Peled ◽  
Benjamin Raichel

2021 ◽  
Vol 144 ◽  
pp. 110745
Author(s):  
Ankit Mishra ◽  
Jayendra N. Bandyopadhyay ◽  
Sarika Jalan

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