## Computation of multiples of Christoffel words. (Calcul de multiples de mots de Christoffel.)(French)Zbl 0827.11015

A Christoffel word $$f$$ is a finite or infinite word on the alphabet $$X= \{0, 1\}$$ such that for each finite prefix $$f'$$ of $$f$$ one has $$\rho (f')= \max\{ \rho(u)$$; $$u\in X^*$$, $$|u|= |f'|$$ and $$\rho (u)\leq \rho (f)\}$$, where $$\rho (u)= |u|_1/ |u|_0\in \mathbb{Q}^+\cup \{+\infty\}$$. If $$f$$ is an infinite Christoffel word, the sequence of $$\rho (f')$$, $$f'$$ a finite prefix of $$f$$, converges to a number $$\rho (f)$$. For each $$\rho\in \mathbb{R}^+\cup \{+\infty\}$$, there is a unique Christoffel word $$f$$ with $$\rho (f)= \rho$$. The authors give an algorithm which transforms $$f$$ into the Christoffel word $$g$$ with $$\rho (g)= p\rho (f)$$, for $$p$$ prime $$\geq 5$$, under certain conditions on the partial quotients of the continued fraction representing $$\rho(f)$$.

### MSC:

 11B85 Automata sequences 68R15 Combinatorics on words 68Q45 Formal languages and automata

### Citations:

Zbl 0768.11024; Zbl 0742.11013