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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2019 Volume 106, Issue 3, Pages 457–467 (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

Language: English


 English version:
Mathematical Notes, 2019, 106:3, 457–467

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© Steklov Math. Inst. of RAS, 2024