Transfinite Lyndon words

Transfinite Lyndon words

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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 detroit tigers throwback hat 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 model 1840 light artillery saber special form and that it can be computed from a rational expression describing the word.