In this paper, we extend the notion of Lyndon word to transfinite words. We prove two main results. We first show that, given a transfinite word, there exists a unique factorization in Lyndon words that are densely non-increasing, a relaxation of the condition used in the case of finite words. In the annex, we prove that the factorization of a rational word has a special form and that it can be computed from a rational expression describing the word.

中文翻译：

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超限林登词

在本文中，我们将林登词的概念扩展到超限词。我们证明了两个主要结果。我们首先证明，给定一个超限词，在 Lyndon 词中存在一个独特的因子分解，它是密集非增加的，这是在有限词的情况下使用的条件的松弛。在附件中，我们证明了有理词的因式分解具有特殊的形式，并且可以从描述该词的有理表达式中计算出来。