Borel, Jean-Pierre; Laubie, François Construction de mots de Christoffel. (Construction of Christoffel words). (French) Zbl 0742.11013 C. R. Acad. Sci., Paris, Sér. I 313, No. 8, 483-485 (1991). The authors first define a (finite) Christoffel word: this is a Lyndon word lexicographically maximal with a given slope. They generalize this notion to infinite Christoffel words, and prove that the action of \(PGL_ 2(\mathbb{Z})\) on \(\mathbb{P}^ 1\) can be identified with the action of certain substitutions on a subset of the set of infinite Christoffel words. This is related to Beatty sequences and Sturmian words, and some applications are announced for a future note. Reviewer: J.-P.Allouche (Bordeaux) Cited in 3 ReviewsCited in 4 Documents MSC: 11B85 Automata sequences 68R15 Combinatorics on words 68Q45 Formal languages and automata 11J70 Continued fractions and generalizations 03D05 Automata and formal grammars in connection with logical questions Keywords:Lyndon word; infinite Christoffel words; substitutions; Beatty sequences; Sturmian word PDF BibTeX XML Cite \textit{J.-P. Borel} and \textit{F. Laubie}, C. R. Acad. Sci., Paris, Sér. I 313, No. 8, 483--485 (1991; Zbl 0742.11013) Online Encyclopedia of Integer Sequences: Fixed point of the morphism 0->01, 1->011.