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    Universal Lyndon Words

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    A word ww over an alphabet Σ\Sigma is a Lyndon word if there exists an order defined on Σ\Sigma for which ww is lexicographically smaller than all of its conjugates (other than itself). We introduce and study \emph{universal Lyndon words}, which are words over an nn-letter alphabet that have length n!n! and such that all the conjugates are Lyndon words. We show that universal Lyndon words exist for every nn and exhibit combinatorial and structural properties of these words. We then define particular prefix codes, which we call Hamiltonian lex-codes, and show that every Hamiltonian lex-code is in bijection with the set of the shortest unrepeated prefixes of the conjugates of a universal Lyndon word. This allows us to give an algorithm for constructing all the universal Lyndon words.Comment: To appear in the proceedings of MFCS 201
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