Cobham's theorem for substitutions
Fabien Durand · Journal of the European Mathematical Society · 2011
The seminal theorem of Cobham has given rise during the last 40 years to a lot of works about non-standard numeration systems and has been extended to many contexts. In this paper, as a result of fifteen years of improvements, we obtain a complete and general version for the so-called substitutive sequences. Let \alpha and \beta be two multiplicatively independent Perron numbers. Then, a sequence x\in A^\mathbb{N} , where A is a finite alphabet, is both \alpha -substitutive and \beta -substitutive if and only if x is ultimately periodic.