The Prague Stringology Conference 2008

Geneviève Paquin

Infinite Smooth Lyndon Words

In a recent paper, Brlek et al. showed that some extremal infinite smooth words are also infinite Lyndon words. This result raises a natural question: what are the infinite smooth words that are also infinite Lyndon words? In this paper, we give the answer: the only infinite smooth Lyndon words are m{a < b}, with a, b even, and m{1 < b}, with b odd, where mA is the minimal infinite smooth word with respect to lexicographic order over the numerical alphabet A.

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