We consider repetitions in words and solve a longstanding open problem about the relation between the period and the length of its longest unbordered factor. A word u is called bordered if there exists a proper prefix that is also a suffix of u, otherwise it is called unbordered. In 1979 Ehrenfeucht and Silberger raised the following problem: What is the maximum length of a word w, w.r.t. the length τ of its longest unbordered factor, still allowing that τ is shorter than the period π of w. We show that if w is longer than 7(τ-1)/3 then τ=π which gives the optimal asymtotic bound. © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Holub, Š., & Nowotka, D. (2009). The ehrenfeucht-silberger problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5555 LNCS, pp. 537–548). https://doi.org/10.1007/978-3-642-02927-1_45
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