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Article Dans Une Revue Journal of Integer Sequences Année : 2014

On a Class of Lyndon Words Extending Christoffel Words and Related to a Multidimensional Continued Fraction Algorithm

Résumé

We de ne a class of Lyndon words, called Christo el-Lyndon words. We show that they are in bijection with n-tuples of relatively prime natural numbers. We give a geometrical interpretation of these words. They are linked to an algorithm of Euclidean type, admitting an extension to n-tuples of real numbers; we show that if the algorithm is periodic, then these real numbers are algebraic of degree at most n and that the associated multidimensional continued fraction converges to these numbers.
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Dates et versions

hal-01002391 , version 1 (06-06-2014)

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  • HAL Id : hal-01002391 , version 1

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Guy Melançon, Christophe Reutenauer. On a Class of Lyndon Words Extending Christoffel Words and Related to a Multidimensional Continued Fraction Algorithm. Journal of Integer Sequences, 2014, 16, pp.13.19.17. ⟨hal-01002391⟩
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