Abstract
Local constraints on an infinite sequence that imply global regularity are of general interest in combinatorics on words. We consider this topic by studying everywhere α -repetitive sequences, sequences in which every position has an occurrence of a repetition of order α ≥ 1 of bounded length. The number of minimal such repetitions, called minimal α -powers, is then finite. A natural question regarding global regularity is to determine the least number of minimal α-powers such that an α-repetitive sequence is not necessarily ultimately periodic. We solve this question for 1 ≤ α ≤ 17/8. We also show that Sturmian words are among the optimal 2 - and 2 + -repetitive sequences.
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Saari, K. (2007). Everywhere α-Repetitive Sequences and Sturmian Words. In: Diekert, V., Volkov, M.V., Voronkov, A. (eds) Computer Science – Theory and Applications. CSR 2007. Lecture Notes in Computer Science, vol 4649. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74510-5_37
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DOI: https://doi.org/10.1007/978-3-540-74510-5_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74509-9
Online ISBN: 978-3-540-74510-5
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