<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We state a new formula to compute the Markoff numbers using iterated palindromic closure and the Thue-Morse substitution. The main theorem shows that for each Markoff number m, there exists a word v ∈ {a, b}∗ such that m − 2 is equal to the length of the iterated palindromic closure of the iterated antipalindromic closure of the word av. This construction gives a new recursive construction of the Markoff numbers by the lengths of the words involved in the palindromic closure. This construction interpolates between the Fibonacci numbers and the Pell numbers.</p></abstract>

We state a new formula to compute the Markoff numbers using iterated palindromic closure and the Thue-Morse substitution. The main theorem shows that for each Markoff number m, there exists a word v ∈ {a, b}∗ such that m − 2 is equal to the length of the iterated palindromic closure of the iterated antipalindromic closure of the word av. This construction gives a new recursive construction of the Markoff numbers by the lengths of the words involved in the palindromic closure. This construction interpolates between the Fibonacci numbers and the Pell numbers.

Palindromic Closures and Thue-Morse Substitution for Markoff Numbers

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Palindromic Closures and Thue-Morse Substitution for Markoff Numbers"}

We state a new formula to compute the Markoff numbers using iterated palindromic closure and the Thue-Morse substitution. The main theorem shows that for each...

Palindromic Closures and Thue-Morse Substitution for Markoff Numbers

Published Online: Jan 30, 2018

Page range: 25 - 35

Received: Aug 07, 2016

Accepted: Jan 20, 2017

DOI: https://doi.org/10.1515/udt-2017-0013

Keywords
iterated palindromic closure, Thue-Morse Substitution, Markoff spectra

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Palindromic Closures and Thue-Morse Substitution for Markoff Numbers

Published Online: Jan 30, 2018

Page range: 25 - 35

Received: Aug 07, 2016

Accepted: Jan 20, 2017

DOI: https://doi.org/10.1515/udt-2017-0013

Keywordsiterated palindromic closure, Thue-Morse Substitution, Markoff spectra

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
iterated palindromic closure, Thue-Morse Substitution, Markoff spectra