We introduce a new very large family of transformations of rectangular diagrams of links that preserve the isotopy class of the link. We provide an example when two diagrams of the same complexity are related by such a transformation and are not obtained from one another by any sequence of “simpler” moves not increasing the complexity of the diagram along the way.

中文翻译：

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Multiflypes 的矩形链接图

我们引入了一个新的非常大的一系列链接矩形图的变换，这些变换保留了链接的同位素类别。我们提供了一个示例，当具有相同复杂性的两个图通过这种转换相关联并且不是通过任何“更简单”的移动序列而不是沿途增加图的复杂性而从另一个图获得时。