Syndeticity and independent substitutions

Details Syndeticity and independent substitutions Syndeticity and independent substitutions

2009-07-27

arxiv.org/abs/0907.4583v1

Advances in Applied Mathematics, 42 (2009) 1-22

Mathematics

Combinatorics

Scientific paper

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 $x$ is generated by two independent substitutions, at least one being of exponential growth, then the factors of $x$ appearing infinitely often in $x$ 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.

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