Selfdual substitutions in dimension one

There are several notions of the ‘dual’ of a word/tile substitution. We show that the most common ones are equivalent for substitutions in dimension one, where we restrict ourselves to the case of two letters/tiles. Furthermore, we obtain necessary and sufficient arithmetic conditions for substitutions being selfdual in this case. Since many connections between the different notions of word/tile substitution are discussed, this paper may also serve as a survey paper on this topic.

► We describe several notions of the ‘dual’ of a word/tile substitution.
► We show that the most common ones are equivalent for two-letter substitutions in dimension one.
► We obtain necessary and sufficient arithmetic conditions for substitutions being selfdual.