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Article Dans Une Revue Theoretical Computer Science Année : 2023

On balanced and abelian properties of circular words over a ternary alphabet

Résumé

We revisit the problem of extending the notion of a balanced circular word and focus on the case of a ternary alphabet. Basing on the fact that the upper bound for the abelian complexity of balanced ternary words is 3 we provide a classification of all circular words over a ternary alphabet with abelian complexity subject to this bound. This result also allows us to construct an uncountable set of bi-infinite aperiodic words with abelian complexity equal to 3.(c) 2022 Elsevier B.V. All rights reserved.

Dates et versions

hal-04479863 , version 1 (27-02-2024)

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D.V. Bulgakova, N. Buzhinsky, Y.O. Goncharov. On balanced and abelian properties of circular words over a ternary alphabet. Theoretical Computer Science, 2023, 939, pp.227-236. ⟨10.1016/j.tcs.2022.10.027⟩. ⟨hal-04479863⟩
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