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Binary patterns in the Prouhet-Thue-Morse sequence

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ALMEIDA Jorge KLÍMA Ondřej

Rok publikování 2021
Druh Článek v odborném periodiku
Časopis / Zdroj Discrete Mathematics and Theoretical Computer Science
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://dmtcs.episciences.org/8398
Doi http://dx.doi.org/10.46298/dmtcs.5460
Klíčová slova Prouhet-Thue-Morse sequence; pattern; infinite word; special word
Popis We show that, with the exception of the words a(2)ba(2) and b(2)ab(2), all (finite or infinite) binary patterns in the Prouhet-Thue-Morse sequence can actually be found in that sequence as segments (up to exchange of letters in the infinite case). This result was previously attributed to unpublished work by D. Guaiana and may also be derived from publications of A. Shur only available in Russian. We also identify the (finitely many) finite binary patterns that appear non trivially, in the sense that they are obtained by applying an endomorphism that does not map the set of all segments of the sequence into itself.
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