We study cube-free words over arbitrary non-unary finite alphabets and prove the following structural property: for every pair (u, v) of d-ary cube-free words, if u can be infinitely extended to the right and v can be infinitely extended to the left respecting the cube-freeness property, then there exists a “transition” word w over the same alphabet such that uwv is cube free. The crucial case is the case of the binary alphabet, analyzed in the central part of the paper. The obtained “transition property”, together with the developed technique, allowed us to solve cube-free versions of three old open problems by Restivo and Salemi. Besides, it has some further implications for combinatorics on words; e.g., it implies the existence of infinite cube-free words of very big subword (factor) complexity.

我们研究任意非一元有限字母上的无立方词，并证明以下结构特性：对于每对（u，v）个d-无立方词，如果u可以无限地向右扩展，并且v可以是相对于cube-freeness属性，可无限扩展到左侧，然后在同一字母上存在一个“过渡”单词w，因此uwv没有立方体。关键案例是二进制字母的案例，在本文的中心部分进行了分析。所获得的“过渡特性”以及发达的技术，使我们能够解决Restivo和Salemi提出的三个老的开放问题的无立方版本。此外，它对单词组合学也有进一步的启示。例如，这意味着存在无限大的子词（因数）复杂度的无立方体词。