Abstract

A word v = wu is a (nontrivial) Duval extension of the unbordered word w, if (u is not a prefix of v and) w is an unbordered factor of v of maximum length. After a short survey of the research topic related to Duval extensions, we show that, if wu is a minimal Duval extension of w, then u is a factor of w. We also show that finite, unbordered factors of Sturmian words are Lyndon words.

Keywords: combinatorics on words, Duval's conjecture, Lyndon words, Sturmian words

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