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@article{1806122, author = {Almeida, Jorge and Klíma, Ondřej}, article_number = {3}, doi = {http://dx.doi.org/10.46298/dmtcs.5460}, keywords = {Prouhet-Thue-Morse sequence; pattern; infinite word; special word}, language = {eng}, issn = {1462-7264}, journal = {Discrete Mathematics and Theoretical Computer Science}, title = {Binary patterns in the Prouhet-Thue-Morse sequence}, url = {https://dmtcs.episciences.org/8398}, volume = {23}, year = {2021} }
TY - JOUR ID - 1806122 AU - Almeida, Jorge - Klíma, Ondřej PY - 2021 TI - Binary patterns in the Prouhet-Thue-Morse sequence JF - Discrete Mathematics and Theoretical Computer Science VL - 23 IS - 3 SP - 1-13 EP - 1-13 PB - Discrete Mathematics and Theoretical Computer Science SN - 14627264 KW - Prouhet-Thue-Morse sequence KW - pattern KW - infinite word KW - special word UR - https://dmtcs.episciences.org/8398 N2 - 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 This result was previously attributed to unpublished work by D. Guaiana and may also be derived from publications of A. Shur only available in Russian.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. ER -
ALMEIDA, Jorge a Ondřej KLÍMA. Binary patterns in the Prouhet-Thue-Morse sequence. \textit{Discrete Mathematics and Theoretical Computer Science}. Discrete Mathematics and Theoretical Computer Science, roč.~23, č.~3, s.~1-13. ISSN~1462-7264. doi:10.46298/dmtcs.5460. 2021.
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