Allauzen: Une caractérisation simple des nombres de Sturm

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Cyril Allauzen
Une caractérisation simple des nombres de Sturm
Journal de théorie des nombres de Bordeaux, 10 no. 2 (1998), p. 237-241, doi: 10.5802/jtnb.226
Article PDF | Reviews MR 1828243 | Zbl 0930.11051 | 1 citation in Cedram

Résumé - Abstract

A sturmian word is the discretization of a straight line with an irrational slope. A sturmian number is the slope of a substitution invariant sturmian word. These numbers are some quadratic irrationals characterized by the form of their continued fraction expansion. We give a very simple characterization of sturmian numbers : a positive irrational number is Sturmian (of the first kind) if and only if it is quadratic with a negative conjugate.

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