Substitution Invariant Sturmian Words and Binary Trees

Michel Dekking

Substitution Invariant Sturmian Words and Binary Trees

Michel Dekking

Applied Probability

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

57 Downloads (Pure)

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.

Original language	English
Article number	A7
Pages (from-to)	1-15
Number of pages	15
Journal	Integers
Volume	18A
Publication status	Published - 2018

Access to Document

46901967Final published version, 255 KB

Cite this

@article{bee082c6c54e4c7bbfe151ef7abb1961,

title = "Substitution Invariant Sturmian Words and Binary Trees",

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{\textquoteright}s tree of harmonic fractions from 1619. We obtain similar results for the inhomogeneous sequences sα,1−α and sα,0.",

author = "Michel Dekking",

year = "2018",

language = "English",

volume = "18A",

pages = "1--15",

journal = "Integers",

issn = "1867-0652",

publisher = "Walter de Gruyter",

}

TY - JOUR

T1 - Substitution Invariant Sturmian Words and Binary Trees

AU - Dekking, Michel

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

UR - http://resolver.tudelft.nl/uuid:bee082c6-c54e-4c7b-bfe1-51ef7abb1961

M3 - Article

SN - 1867-0652

VL - 18A

SP - 1

EP - 15

JO - Integers

JF - Integers

M1 - A7

ER -

Substitution Invariant Sturmian Words and Binary Trees

Abstract

Access to Document

Other files and links

Fingerprint

Cite this