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ЖУРНАЛЫ // Математические заметки // Архив

Матем. заметки, 2019, том 106, выпуск 3, страницы 457–467 (Mi mzm12583)

Статьи, опубликованные в английской версии журнала

Palindromic Sequences of the Markov Spectrum

M. van Son

University of Liverpool, Liverpool, L69 3BX United Kingdom

Аннотация: 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.

Ключевые слова: Markov sequence, Stern's diatomic series, Stern's diatomic sequence, palindromic sequence, evenly palindromic, Christoffel words.

Поступило: 02.01.2019

Язык публикации: английский


 Англоязычная версия: Mathematical Notes, 2019, 106:3, 457–467

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