A generalization of Cobham's Theorem

Fabien Durand

Published 2008-07-22Version 1

If a non-periodic sequence $X$ is the image by a morphism of a fixed point of both a primitive substitution $\sigma$ and a primitive substitution $\tau$, then the dominant eigenvalues of the matrices of $\sigma$ and of $\tau$ are multiplicatively dependent. This is the way we propose to generalize Cobham's Theorem.