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Christoffel Words

In: Markov's Theorem and 100 Years of the Uniqueness Conjecture

Author

Listed:
  • Martin Aigner

    (Freie Universität Berlin, Fachbereich Mathematik und Informatik Institut für Mathematik)

Abstract

We have seen in the previous chapter that Cohn matrices may be regarded as words W t in the free group SL( $$2, \mathbb{Z}$$ )’, generated by any starting pair A and B. In this chapter, we want to derive a beautiful geometric description of Cohn words that will prepare the ground for a combinatorial approach to Markov’s theorem. By this we mean the following: We know that for an irrational number α with Lagrange number L(α

Suggested Citation

  • Martin Aigner, 2013. "Christoffel Words," Springer Books, in: Markov's Theorem and 100 Years of the Uniqueness Conjecture, edition 127, chapter 7, pages 135-157, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-00888-2_7
    DOI: 10.1007/978-3-319-00888-2_7
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