Two-block substitutions and morphic words

Michel Dekking; Michael Keane

doi:10.1016/j.aam.2023.102536

Two-block substitutions and morphic words

Michel Dekking^*, Michael Keane

^*Corresponding author for this work

Applied Probability

Research output: Contribution to journal › Article › Scientific › peer-review

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Abstract

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.

Original language	English
Article number	102536
Number of pages	8
Journal	Advances in Applied Mathematics
Volume	148
DOIs	https://doi.org/10.1016/j.aam.2023.102536
Publication status	Published - 2023

Keywords

Base 3/2
Kolakoski sequence
Morphic words
Two-block substitutions

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10.1016/j.aam.2023.102536

1-s2.0-S0196885823000544-mainFinal published version, 251 KBLicence: CC BY

Cite this

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title = "Two-block substitutions and morphic words",

abstract = "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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AU - Dekking, Michel

AU - Keane, Michael

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AB - 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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KW - Kolakoski sequence

KW - Morphic words

KW - Two-block substitutions

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U2 - 10.1016/j.aam.2023.102536

DO - 10.1016/j.aam.2023.102536

M3 - Article

AN - SCOPUS:85152120404

SN - 0196-8858

VL - 148

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

M1 - 102536

ER -

Two-block substitutions and morphic words

Abstract

Keywords

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