Episturmian words : a survey
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 43 (2009) no. 3, p. 403-442

In this paper, we survey the rich theory of infinite episturmian words which generalize to any finite alphabet, in a rather resembling way, the well-known family of sturmian words on two letters. After recalling definitions and basic properties, we consider episturmian morphisms that allow for a deeper study of these words. Some properties of factors are described, including factor complexity, palindromes, fractional powers, frequencies, and return words. We also consider lexicographical properties of episturmian words, as well as their connection to the balance property, and related notions such as finite episturmian words, Arnoux-Rauzy sequences, and “episkew words” that generalize the skew words of Morse and Hedlund.

DOI : https://doi.org/10.1051/ita/2009003
Classification:  68R15
Keywords: combinatorics on words, episturmian words, Arnoux-Rauzy sequences, sturmian words, episturmian morphisms
@article{ITA_2009__43_3_403_0,
     author = {Glen, Amy and Justin, Jacques},
     title = {Episturmian words : a survey},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {3},
     year = {2009},
     pages = {403-442},
     doi = {10.1051/ita/2009003},
     zbl = {pre05578831},
     mrnumber = {2541129},
     language = {en},
     url = {http://www.numdam.org/item/ITA_2009__43_3_403_0}
}
Glen, Amy; Justin, Jacques. Episturmian words : a survey. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 43 (2009) no. 3, pp. 403-442. doi : 10.1051/ita/2009003. http://www.numdam.org/item/ITA_2009__43_3_403_0/

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