Transcendence of dendric beta-expansions with pure discrete spectrum

Abstract

We prove the transcendence of numbers that have $\beta$-expansions (in algebraic bases $\beta$) belonging to dendric shifts with pure discrete spectrum, under combinatorial conditions on their directive sequences of substitutions. This includes Arnoux-Rauzy sequences on arbitrary alphabets and Cassaigne-Selmer sequences. The proof uses Rauzy fractals and the subspace theorem.