Substitutive systems and a finitary version of Cobham's theorem
Combinatorics
2020-09-23 v2 Formal Languages and Automata Theory
Dynamical Systems
Number Theory
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.
Cite
@article{arxiv.1908.11244,
title = {Substitutive systems and a finitary version of Cobham's theorem},
author = {Jakub Byszewski and Jakub Konieczny and Elżbieta Krawczyk},
journal= {arXiv preprint arXiv:1908.11244},
year = {2020}
}
Comments
23 pages. v2: incorporates referee's comments, updated references, to appear in Combinatorica