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Article Dans Une Revue Notes on Number Theory and Discrete Mathematics Année : 2023

On ternary Dejean words avoiding 010

Résumé

Thue has shown the existence of three types of infinite square-free words over {0,1,2} avoiding the factor 010. They respectively avoid {010,212}, {010,101}, and {010,020}. Also Dejean constructed an infinite $\left(\tfrac74^+\right)$-free ternary word. A word is $d$-directed if it does not contain both a factor of length $d$ and its mirror image. We show that there exist exponentially many $\left(\tfrac74^+\right)$-free 180-directed ternary words avoiding 010. Moreover, there does not exist an infinite $\left(\tfrac74^+\right)$-free 179-directed ternary word avoiding 010.

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hal-04241523 , version 1 (14-10-2023)

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Pascal Ochem. On ternary Dejean words avoiding 010. Notes on Number Theory and Discrete Mathematics, 2023, 29 (3), pp.545-548. ⟨10.7546/nntdm.2023.29.3.545-548⟩. ⟨hal-04241523⟩
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