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    Algorithms to test open set condition for self-similar set related to P.V. numbers

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    Fix a P.V. number Ξ»βˆ’1>1.\lambda ^{-1}>1. Given p=(p1,⋯ ,pm)∈Nm\mathbf{p}=(p_{1},\cdots,p_{m})\in \mathbb{N}^{m}, \mathbf{b}=(b_{1},\cdots,b_{m})\in \mathbb{Q^{m}, for the self-similar set Ep,b=βˆͺi=1m(Ξ»piEp,b+bi)E_{\mathbf{p},\mathbf{b}}=\cup_{i=1}^{m}(\lambda ^{p_{i}}E_{\mathbf{p},\mathbf{b}}+b_{i}) we find an efficient algorithm to test whether Ep,bE_{\mathbf{p},\mathbf{b}} satisfies the open set condition (strong separation condition) or not
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