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Locally Periodic Versus Globally Periodic Infinite Words

✍ Scribed by J. Karhumäki; A. Lepistö; W. Plandowski

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 164 KB
Volume: 100
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.2002.3292

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✦ Synopsis

We call a one-way infinite word w over a finite alphabet ðr; lÞ-repetitive if all long enough prefixes of w contain as a suffix a rth power (or more generally a repetition of order r) of a word of length at most l: We show that each ð2; 4Þrepetitive word is ultimately periodic, as well as that there exist continuum many, and hence also nonultimately periodic, ð2; 5Þ-repetitive words. Further, we characterize nonultimately periodic ð2; 5Þ-repetitive words both structurally and algebraically.

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