In this paper, we extend the notion of Lyndon word to transfinite words. Weprove two main results. We first show that, given a transfinite word, thereexists 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 aspecial form and that it can be computed from a rational expression describingthe word.
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