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Words and Quadratic Numbers
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This chapter offers an overview of words and quadratic numbers, and in particular ordering the conjugates of a Christoffel word. Within this topic the reader learns that the reversal of a Christoffel word is a conjugate, and that the lower and upper Christoffel words of the same slope are the smallest and the largest in their conjugation class. The chapter discusses computation in terms ofMarkoff numbers of the quadratic real number which has a periodic continued fraction with periodic pattern equal to a Christoffel word written on the alphabet 11, 22. It also reviews computation of theMarkoff supremum of a periodic biinfinite sequence, and of theLagrange number of a periodic sequence, both having a periodic pattern as above.
Title: Words and Quadratic Numbers
Description:
This chapter offers an overview of words and quadratic numbers, and in particular ordering the conjugates of a Christoffel word.
Within this topic the reader learns that the reversal of a Christoffel word is a conjugate, and that the lower and upper Christoffel words of the same slope are the smallest and the largest in their conjugation class.
The chapter discusses computation in terms ofMarkoff numbers of the quadratic real number which has a periodic continued fraction with periodic pattern equal to a Christoffel word written on the alphabet 11, 22.
It also reviews computation of theMarkoff supremum of a periodic biinfinite sequence, and of theLagrange number of a periodic sequence, both having a periodic pattern as above.
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