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.

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
Mots-clés : Thue-Morse word, overlap-free word, automatic sequence 
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     title = {Squares and overlaps in the {Thue-Morse} sequence and some variants},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
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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. http://archive.numdam.org/articles/10.1051/ita:2006030/

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