Geodesic
Squares and overlaps in the Thue-Morse sequence and some variants
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 3, pp. 473-484

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We consider the position and number of occurrences of squares in the Thue-Morse sequence, and show that the corresponding sequences are 2-regular. We also prove that changing any finite but nonzero number of bits in the Thue-Morse sequence creates an overlap, and any linear subsequence of the Thue-Morse sequence (except those corresponding to decimation by a power of 2) contains an overlap.

DOI : 10.1051/ita:2006030
Classification : 68Q45, 68R15
Keywords: Thue-Morse word, overlap-free word, automatic sequence 
@article{ITA_2006__40_3_473_0,
     author = {Brown, Shandy and Rampersad, Narad and Shallit, Jeffrey and Vasiga, Troy},
     title = {Squares and overlaps in the {Thue-Morse} sequence and some variants},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {473--484},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {3},
     year = {2006},
     doi = {10.1051/ita:2006030},
     mrnumber = {2269205},
     zbl = {1110.68117},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita:2006030/}
}
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Brown, Shandy; Rampersad, Narad; Shallit, Jeffrey; Vasiga, Troy. Squares and overlaps in the Thue-Morse sequence and some variants. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 3, pp. 473-484. doi: 10.1051/ita:2006030

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