<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

Publié en ligne: 30 janv. 2018

Pages: 25 - 35

Reçu: 07 août 2016

Accepté: 20 janv. 2017

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

Mots clés
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

Publié en ligne: 30 janv. 2018

Pages: 25 - 35

Reçu: 07 août 2016

Accepté: 20 janv. 2017

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

Mots clésiterated palindromic closure, Thue-Morse Substitution, Markoff spectra

© 2018

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

Mots clés
iterated palindromic closure, Thue-Morse Substitution, Markoff spectra