Two-block substitutions and morphic words

Two-block substitutions and morphic words

We consider in general two-block substitutions and their fixed points. We prove that some of them have a simple structure: their fixed points are morphic sequences. Others are intrinsically more complex, such as the Kolakoski sequence. We prove this for the Thue-Morse sequence in base 3/2.

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Veröffentlicht in:Advances in applied mathematics 2023-07, Vol.148, p.102536, Article 102536
Hauptverfasser: Dekking, Michel, Keane, Michael
Format: Artikel
Sprache:eng
Schlagworte:
Base 3/2
Kolakoski sequence
Morphic words
Two-block substitutions
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Beschreibung
Zusammenfassung:We consider in general two-block substitutions and their fixed points. We prove that some of them have a simple structure: their fixed points are morphic sequences. Others are intrinsically more complex, such as the Kolakoski sequence. We prove this for the Thue-Morse sequence in base 3/2.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2023.102536