Substitutive systems and a finitary version of Cobham's theorem

Abstract

We study substitutive systems generated by nonprimitive substitutions and show that transitive subsystems of substitutive systems are substitutive. As an application we obtain a complete characterisation of the sets of words that can appear as common factors of two automatic sequences defined over multiplicatively independent bases. This generalises the famous theorem of Cobham.

arXiv comment23 pages. v2: incorporates referee's comments, updated references, to appear in Combinatorica