Syndeticity and independent substitutions
Combinatorics
2009-07-28 v1 Discrete Mathematics
Abstract
We associate in a canonical way a substitution to any abstract numeration system built on a regular language. In relationship with the growth order of the letters, we define the notion of two independent substitutions. Our main result is the following. If a sequence is generated by two independent substitutions, at least one being of exponential growth, then the factors of appearing infinitely often in appear with bounded gaps. As an application, we derive an analogue of Cobham's theorem for two independent substitutions (or abstract numeration systems) one with polynomial growth, the other being exponential.
Keywords
Cite
@article{arxiv.0907.4583,
title = {Syndeticity and independent substitutions},
author = {Fabien Durand and Michel Rigo},
journal= {arXiv preprint arXiv:0907.4583},
year = {2009}
}