About Duval's Conjecture
نویسندگان
چکیده
A word is called unbordered, if it has no proper prefix which is also a suffix of that word. Let μ(w) denote the length of the longest unbordered factor of a word w. Let a word where the longest unbordered prefix is equal to μ(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 3μ(w)−4 is trivial. We improve that bound to 5μ(w)/2−1 in this paper, and with that, move closer to the bound 2μ(w) conjectured by Duval. Our proof also contains a natural application of the Critical Factorization Theorem.
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