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.

@article{abs-1809-09033,
  title = {Transfinite Lyndon words},
  author = {Olivier Carton and Luc Boasson},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 16, Issue 4},
  year = {2020},
  doi = {10.23638/lmcs-16(4:9)2020}
}