Article
Palindromic Closures and Thue-Morse Substitution for Markoff Numbers
Authors
and
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.
Keywords
iterated palindromic closure, Thue-Morse Substitution, Markoff spectra.
Citation
Reutenauer, C. & Vuillon, L. (2017). Palindromic closures and thue-morse substitution for markoff numbers. Uniform Distribution Theory, 12(2), 25–35. https://doi.org/10.1515/udt-2017-0013
C. Reutenauer and L. Vuillon, “Palindromic closures and thue-morse substitution for markoff numbers,” Uniform Distribution Theory, vol. 12, no. 2, pp. 25–35, 2017, doi: 10.1515/udt-2017-0013.
Reutenauer C, Vuillon L. Palindromic closures and thue-morse substitution for markoff numbers. Uniform Distribution Theory. 2017;12(2):25–35. doi:10.1515/udt-2017-0013.
Reutenauer, C. and Vuillon, L. (2017), ‘Palindromic closures and thue-morse substitution for markoff numbers’, Uniform Distribution Theory, 12(2), pp. 25–35. Available at: https://doi.org/10.1515/udt-2017-0013.
Reutenauer, Christophe, and Laurent Vuillon. “Palindromic Closures and Thue-morse Substitution for Markoff Numbers.” Uniform Distribution Theory, vol. 12, no. 2, 2017, pp. 25–35. https://doi.org/10.1515/udt-2017-0013.
Reutenauer, Christophe, and Laurent Vuillon. “Palindromic Closures and Thue-morse Substitution for Markoff Numbers.” Uniform Distribution Theory 12, no. 2 (2017): 25–35. https://doi.org/10.1515/udt-2017-0013.
Export citation
Published by: Engineering Journals
