Selfdual Substitutions in Dimension One

Details Selfdual Substitutions in Dimension One Selfdual Substitutions in Dimension One

2011-08-25

arxiv.org/abs/1108.5053v2

Mathematics

Combinatorics

28 pages, 5 figures. Several typos removed, some proofs shortened, thanks to the referees. The accepted version of this paper

Scientific paper

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.

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