Avoiding conjugacy classes on the 5-letter alphabet

Golnaz Badkobeh (1) , Pascal Ochem (2)

1 Department of Informatics [King's College London]
2 ALGCO - Algorithmes, Graphes et Combinatoire

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].

Mots clés: Combinatorics on words; Conjugacy classes

Domaines: Mathématiques [math]

Golnaz Badkobeh, Pascal Ochem. Avoiding conjugacy classes on the 5-letter alphabet. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), 2020, 54 (2), pp.1-4. ⟨10.1051/ita/2020003⟩. ⟨hal-02903902⟩