scholarly journals On representations of graphs as two-distance sets

2020 ◽  
Vol 343 (1) ◽  
pp. 111587
Author(s):  
A.Y. Alfakih
Keyword(s):  
Distance Sets

On the Hausdorff dimensions of distance sets

Mathematika ◽  
1985 ◽  
Vol 32 (2) ◽  
pp. 206-212 ◽  
Author(s):  
K. J. Falconer
Keyword(s):  
Hausdorff Dimensions ◽  
Distance Sets

Hausdorff dimension and distance sets

1994 ◽  
Vol 87 (1-3) ◽  
pp. 193-201 ◽  
Author(s):  
Jean Bourgain
Keyword(s):  
Hausdorff Dimension ◽  
Distance Sets

scholarly journals Dimension approximation of attractors of graph directed IFSs by self-similar sets

2018 ◽  
Vol 167 (01) ◽  
pp. 193-207 ◽  
Author(s):  
ÁBEL FARKAS
Keyword(s):  
Iterated Function System ◽  
Black Box ◽  
Function System ◽  
Separation Condition ◽  
Iterated Function ◽  
Strong Separation ◽  
Self Similar ◽  
Strong Separation Condition ◽  
Distance Sets

AbstractWe show that for the attractor (K1, . . ., Kq) of a graph directed iterated function system, for each 1 ⩽ j ⩽ q and ϵ > 0 there exists a self-similar set K ⊆ Kj that satisfies the strong separation condition and dimHKj − ϵ < dimHK. We show that we can further assume convenient conditions on the orthogonal parts and similarity ratios of the defining similarities of K. Using this property as a ‘black box’ we obtain results on a range of topics including on dimensions of projections, intersections, distance sets and sums and products of sets.

scholarly journals Maximal 2-distance sets containing the regular simplex

2020 ◽  
Vol 343 (11) ◽  
pp. 112071
Author(s):  
Hiroshi Nozaki ◽  
Masashi Shinohara
Keyword(s):  
Regular Simplex ◽  
Distance Sets
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