Adamczewski Boris & Cassaigne Julien

On the transcendence of real numbers with a regular expansion.

We apply the Ferenczi-Mauduit combinatorial condition obtained via a reformulation on a Ridout's theorem to prove that a real number whose $b$-ary expansion is the coding of an irrational rotation on the circle with respect to a partition in two intervals is transcendental. We also prove the transcendence of real numbers whose $b$-ary expansion arises from a non-periodic three-interval exchange transformation.