Locally periodic versus globally periodic infinite words

Authors:
J. Karhumäki;A. Lepistö;W. Plandowski
Affiliations:
Department of Mathematics, University of Turku, 20014 Turku, Finland, and Turku Centre for Computer Science, Finland;Department of Mathematics, University of Turku, 20014 Turku, Finland, and Turku Centre for Computer Science, Finland;Instytut Informatyki, Uniwersytet Warszawski ul. Banacha 2, 02-097, Warsaw, Poland
Venue:
Journal of Combinatorial Theory Series A
Year:
2002

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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.