The $q$-analog of the Markoff injectivity conjecture over the language of a balanced sequence

Sébastien Labbé, Mélodie Lapointe

The Markoff injectivity conjecture states that $w\mapsto \mu (w{)}_{12}$ is injective on the set of Christoffel words where $\mu :\{0,1{\}}^{\ast }\to {\mathrm{SL}}_2(\mathbb{Z})$ is…