Gaps in the Thue-Morse word
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in: Journal of the Australian Mathematical Society, Jahrgang 114.2023, Nr. 1, 25.02.2023, S. 110-144.
Publikationen: Beitrag in Fachzeitschrift › Artikel › Forschung › (peer-reviewed)
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TY - JOUR
T1 - Gaps in the Thue-Morse word
AU - Spiegelhofer, Lukas
N1 - Publisher Copyright: © The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
PY - 2023/2/25
Y1 - 2023/2/25
N2 - The Thue–Morse sequence is a prototypical automatic sequence found in diverse areas of mathematics, and in computer science. We study occurrences of factors w within this sequence, or more precisely, the sequence of gaps between consecutive occurrences. This gap sequence is morphic; we prove that it is not automatic as soon as the length of w is at least 2 , thereby answering a question by J. Shallit in the affirmative. We give an explicit method to compute the discrepancy of the number of occurrences of the block 01 in the Thue–Morse sequence. We prove that the sequence of discrepancies is the sequence of output sums of a certain base- 2 transducer.
AB - The Thue–Morse sequence is a prototypical automatic sequence found in diverse areas of mathematics, and in computer science. We study occurrences of factors w within this sequence, or more precisely, the sequence of gaps between consecutive occurrences. This gap sequence is morphic; we prove that it is not automatic as soon as the length of w is at least 2 , thereby answering a question by J. Shallit in the affirmative. We give an explicit method to compute the discrepancy of the number of occurrences of the block 01 in the Thue–Morse sequence. We prove that the sequence of discrepancies is the sequence of output sums of a certain base- 2 transducer.
UR - http://www.scopus.com/inward/record.url?scp=85124048462&partnerID=8YFLogxK
U2 - 10.1017/S1446788721000380
DO - 10.1017/S1446788721000380
M3 - Article
VL - 114.2023
SP - 110
EP - 144
JO - Journal of the Australian Mathematical Society
JF - Journal of the Australian Mathematical Society
SN - 1446-1811
IS - 1
ER -