Lyndon Words and Singular Factors of Sturmian Words

Abstract Two different factorizations of the Fibonacci infinite word were given independently in Wen and Wen (1994) and Melancon (1996). In a certain sense, these factorizations reveal a selfsimilarity property of the Fibonacci word. We first describe the intimate links between these two factorizations. We then propose a generalization to characteristic sturmian words.