The properties of the intersection of Rauzy fractals associated with substitutions having the same incidence matrix have been studied by several authors. Different techniques have been introduced and used for this purpose, one of them is the balanced pair algorithm. In the present paper we explore the actual limitations of this algorithm. We show that the balanced pair algorithm is defined and terminates only when the intersection of the Rauzy fractals have non-empty interior and when this condition fails it cannot be used.

中文翻译：

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具有相同入射矩阵的量测不相交Rauzy分形

几位作者已经研究了与具有相同入射矩阵的代换相关的Rauzy分形的相交性质。已经引入了各种技术并将其用于此目的，其中一种是平衡对算法。在本文中，我们探索了该算法的实际局限性。我们表明，只有当Rauzy分形的交集具有非空内部并且当此条件失败时，才可以使用平衡对算法并终止。