Locally Periodic Versus Globally Periodic Infinite Words |
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Authors: | J Karhumki A Lepist W Plandowski |
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Institution: | a Department of Mathematics, University of Turku, 20014, Turku, Finland, and Turku Centre for Computer Science, Finland, f1;b Instytut Informatyki, Uniwersytet Warszawski ul. Banacha 2, 02-097, Warsaw, Polandf2 |
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Abstract: | We call a one-way infinite word w over a finite alphabet (ρ,l)-repetitive if all long enough prefixes of w contain as a suffix a ρth power (or more generally a repetition of order ρ) of a word of length at most l. We show that each (2,4)-repetitive word is ultimately periodic, as well as that there exist continuum many, and hence also nonultimately periodic, (2,5)-repetitive words. Further, we characterize nonultimately periodic (2,5)-repetitive words both structurally and algebraically. |
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Keywords: | infinite words periodicity |
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