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What is the Hausdorff dimension of the subset $$F := \{ x = \sum^\infty_{n=1} \frac{2 x_n}{3^n} \in [0,1] : x_n \in \{ 0 , 1 \} , x_n = 1 \Rightarrow x_{n+1}=0 \}$$ of the Cantor set? Is it known already? As far as I know, this set can be corresponded to a binary tree related to the Fibonacci sequence. (I don't know how to call that tree.) Edit: $x_n = 1 \Rightarrow x_{n+1}=0$. |
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What is the Hausdorff dimension of the subset $$F := \{ x = \sum^\infty_{n=1} \frac{2 x_n}{3^n} \in [0,1] : x_n \in \{ 0 , 1 \} , x_n = 1 \Rightarrow x_{n+1}=0 \}$$ of the Cantor set? Is it known already? As far as I know, this set can be corresponded to a binary tree related to the Fibonacci sequence. (I don't know how to call that tree.) Edit: $x_n = 1 \Rightarrow x_{n+1}=0$. |
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What is the Hausdorff dimension of the subset $$F := \{ x = \sum^\infty_{n=1} \frac{2 x_n}{3^n} \in [0,1] : x_n \in \{ 0 , 1 \} , x_n = 1 \Rightarrow x_n=0 x_{n+1}=0 \}$$ of the Cantor set? Is it known already? As far as I know, this set can be corresponded to a binary tree related to the Fibonacci sequence. (I don't know how to call that tree.) |
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