Avoiding conjugacy classes on the 5-letter alphabet
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 54 (2020), article no. 2.

We construct an infinite word w over the 5-letter alphabet such that for every factor f of w of length at least two, there exists a cyclic permutation of f that is not a factor of w. In other words, w does not contain a non-trivial conjugacy class. This proves the conjecture in Gamard et al. [Theoret. Comput. Sci. 726 (2018) 1–4].

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DOI : 10.1051/ita/2020003
Classification : 68R15
Mots-clés : Combinatorics on words, conjugacy classes 
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Badkobeh, Golnaz; Ochem, Pascal. Avoiding conjugacy classes on the 5-letter alphabet. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 54 (2020), article no. 2. doi : 10.1051/ita/2020003. http://www.numdam.org/articles/10.1051/ita/2020003/

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