# Selfdual substitutions in dimension One

## Valérie Berthé, Dirk Frettlöh, Victor Sirvent – 2012

Focus Area 1: High-complexity Geometry 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.

Title

Selfdual substitutions in dimension One

Author

Valérie Berthé, Dirk Frettlöh, Victor Sirvent

Date

2012-08

Source(s)

Appeared in

European Journal of Combinatorics 33 (2012) 981-1000

Type

Text