Substitution Invariant Sturmian Words and Binary Trees
Michel Dekking (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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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.