The exponent of repetition of the characteristic Sturmian word whose slope is a quadratic irrational

Takao Watanabe

For an infinite word $x$, Bugeaud and Kim introduced a quantity $\mathrm{rep}(x)$ called the exponent of repetition of $x$. We prove that $\mathrm{rep}(x)=\mathrm{rep}(y)$ holds…