Construction de mots de Christoffel. (Construction of Christoffel words). (French) Zbl 0742.11013

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.


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

Online Encyclopedia of Integer Sequences:

Fixed point of the morphism 0->01, 1->011.