Substitution Invariant Sturmian Words and Binary Trees
Journal Article
(2018)
Author(s)
Michel Dekking (TU Delft - Applied Probability)
Research Group
Applied Probability
Copyright
© 2018 F.M. Dekking
To reference this document use:
https://resolver.tudelft.nl/uuid:bee082c6-c54e-4c7b-bfe1-51ef7abb1961
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Publication Year
2018
Language
English
Copyright
© 2018 F.M. Dekking
Research Group
Applied Probability
Volume number
18A
Pages (from-to)
1-15
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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.