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Mathematical Notes

, Volume 106, Issue 3–4, pp 457–467 | Cite as

Palindromic Sequences of the Markov Spectrum

  • M. van SonEmail author
Article
  • 11 Downloads

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 

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Notes

Acknowledgments

The author is grateful to O. Karpenkov for his constant attention to this work.

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.University of LiverpoolLiverpoolUnited Kingdom

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