Propriétés combinatoires et arithmétiques de certaines suites automatiques et substitutives

Abstract : This thesis studies some links between the combinatorial properties of the base-b expansion or of the continued fraction expansion of a given real number and the fact that this real number is algebraic or transcendental (a conjecture of Borel predicts that every irrational algebraic is an absolutely normal number: its base-b expansions have the properties of a random sequence).
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Julien Albert. Propriétés combinatoires et arithmétiques de certaines suites automatiques et substitutives. Combinatoire [math.CO]. Université Paris Sud - Paris XI, 2006. Français. ⟨tel-00820430⟩

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