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Matematicheskie Zametki, 2019, Volume 106, Issue 3, paper published in the English version journal (Mi mzm12583)  
Papers published in the English version of the journal

Palindromic Sequences of the Markov Spectrum

M. van Son

University of Liverpool, Liverpool, L69 3BX United Kingdom
Abstract: We study the periods of Markov sequences, which are derived from the continued fraction expression of elements in the Markov spectrum. This spectrum is the set of minimal values of indefinite binary quadratic forms that are specially normalised. We show that the periods of these sequences are palindromic after a number of circular shifts, the number of shifts being given by Stern's diatomic sequence.
Keywords: Markov sequence, Stern's diatomic series, Stern's diatomic sequence, palindromic sequence, evenly palindromic, Christoffel words.
Received: 02.01.2019
English version:
Mathematical Notes, 2019, Volume 106, Issue 3, Pages 457–467
DOI: https://doi.org/10.1134/S0001434619090153
Bibliographic databases:
Document Type: Article
Language: English
Citation: M. van Son, “Palindromic Sequences of the Markov Spectrum”, Math. Notes, 106:3 (2019), 457–467
Citation in format AMSBIB
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\by M.~van Son
\paper Palindromic Sequences of the Markov Spectrum
\jour Math. Notes
\yr 2019
\vol 106
\issue 3
\pages 457--467
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\crossref{https://doi.org/10.1134/S0001434619090153}
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