The Markoff equation is the Diophantine equation $x^2+y^2+z^2=3xyz$. A solution is called a Markoff triple. We give a bijection between the free monoid on two letters and the set of Markoff triples, using the palindromization map of Aldo de Luca. In our construction, special Christoffel words appear, whose lengths are Markoff numbers; we study their standard and palindromic factorizations, and show that they are self-dual.

中文翻译：

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重印：Palindromization和Markoff三元组的构造

Markoff方程是Diophantine方程 $X^2+{ÿ}^2+{ž}^2=3Xÿž$。一个解决方案称为Markoff三元组。我们使用阿尔多·德·卢卡（Aldo de Luca）的古板化图，给出了两个字母上的自由半体像与Markoff三元组之间的双射。在我们的结构中，出现了特殊的Christoffel单词，其长度为Markoff数；我们研究了它们的标准和回文分解，并表明它们是自对偶的。