Substitution Invariant Sturmian Words and Binary Trees

Journal article (2018)

Authors

F.M. Dekking Applied Probability - EEMCS
Research Group
Applied Probability (EEMCS) (TU Delft)
Copyright: © 2018 F.M. Dekking
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Published Date

2018

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

Abstract

We take a global view at substitution invariant Sturmian sequences. We show that
homogeneous substitution invariant Sturmian sequences sα,α can be indexed by two
binary trees, associated directly with Johannes Kepler’s tree of harmonic fractions
from 1619. We obtain similar results for the inhomogeneous sequences sα,1−α and
sα,0.

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