| Issue |
RAIRO-Theor. Inf. Appl.
Volume 40, Number 3, July-September 2006
Word Avoidability Complexity And Morphisms (WACAM)
|
|
|---|---|---|
| Page(s) | 473 - 484 | |
| DOI | https://doi.org/10.1051/ita:2006030 | |
| Published online | 18 October 2006 | |
Squares and overlaps in the Thue-Morse sequence and some variants
1
Digital Thinkery, 199 Carter Avenue, Waterloo, Ontario N2J 3K5,
Canada; shandy@geeky.net
2
School of Computer Science, University of Waterloo,
Waterloo, Ontario, N2L 3G1, Canada;
nrampersad@math.uwaterloo.ca;
shallit@graceland.uwaterloo.ca; tmjvasiga@cs.uwaterloo.ca
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.
Mathematics Subject Classification: 68Q45 / 68R15
Key words: Thue-Morse word / overlap-free word / automatic sequence.
© EDP Sciences, 2006
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