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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.

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
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