Harju, Tero and Nowotka, Dirk (2003) About Duval’s Conjecture. [Paper] In: Developments in Language Theory (DLT). , 7 - 11 July 2003, Szeged, Hungary . Developments in Language Theory. ; pp. 316-324 . DOI 10.1007/3-540-45007-6_25. Lecture Notes in Computer Science .

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Abstract

A word is called unbordered, if it has no proper prefix which is also a suffix of that word. Let u(w) denote the length of the longest unbordered factor of a word w. Let a word where the longest unbordered prefix is equal to u(w) be called Duval extension. A Duval extension is called trivial, if its longest unbordered factor is of the length of the period of that Duval extension.

In 1982 it was shown by Duval that every Duval extension w longer than 3u(w)-4 is trivial. We improve that bound to 5u(w)/2-1 in this paper, and with that, move closer to the bound 2u(w) conjectured by Duval. Our proof also contains a natural application of the Critical Factorization Theorem.

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