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. Key words: Lyndon words, smooth words, Kolakoski sequence

• Type: Conference
• Year: 2008
• Where: STRINGOLOGY
• Authors: Geneviève Paquin
• Keywords: Infinite Lyndon Words, Infinite Smooth Word, Lyndon Words, Programming Languages, STRINGOLOGY 2008