Authors: Srečko Brlek ¹; Guy Melançon ²; Geneviève Paquin ³

• 1 Laboratoire de combinatoire et d'informatique mathématique [Montréal]
• 2 Laboratoire Bordelais de Recherche en Informatique
• 3 Laboratoire de Mathématiques

Smooth words are connected to the Kolakoski sequence. We construct the maximal and the minimal in nite smooth words, with respect to the lexicographical order. The naive algorithm generating them is improved by using a reduction of the De Bruijn graph of their factors. We also study their Lyndon factorizations. Finally, we show that the minimal smooth word over the alphabet f1; 3g belongs to the orbit of the Fibonacci word.