初等分形几何。5. 弱分离即强分离
Elementary fractal geometry. 5. Weak separation is strong separation
AI总结：
本文研究自相似集的分离条件，证明有限型自相似集可转化为满足开集条件的图导向构造，并以表现良好的组合算法支撑证明。
摘要：
对于自相似集，存在两个重要的分离性质：开集条件，以及由 Zerner 引入的弱分离条件；后者可由形式上更强的 Ngai–Wang 有限型性质替代。我们证明，任何有限型自相似集都能表示为满足开集条件的图导向构造。该证明基于一种组合算法，且该算法在计算机实验中表现良好。
英文摘要：
For self-similar sets, there are two important separation properties: the open set condition and the weak separation condition introduced by Zerner, which may be replaced by the formally stronger finite type property of Ngai and Wang. We show that any finite type self-similar set can be represented as a graph-directed construction obeying the open set condition. The proof is based on a combinatorial algorithm which performed well in computer experiments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
