Selfdual Substitutions in Dimension One

Abstract

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.Comment: 28 pages, 5 figures. Several typos removed, some proofs shortened, thanks to the referees. The accepted version of this paper is shorter (22 pages, 4 figures), this arxiv version includes more examples, two appendices, plus a self-contained proof of Theorem 2.