RAIRO-Theor. Inf. Appl.
Volume 40, Number 3, July-September 2006Word Avoidability Complexity And Morphisms (WACAM)
|Page(s)||473 - 484|
|Published online||18 October 2006|
Squares and overlaps in the Thue-Morse sequence and some variants
Digital Thinkery, 199 Carter Avenue, Waterloo, Ontario N2J 3K5,
2 School of Computer Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada; firstname.lastname@example.org; email@example.com; firstname.lastname@example.org
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.