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Nous établissons quelques propriétés des mots sturmiens et classifions, ensuite, les mots infinis qui possèdent, pour tout entier naturel non nul n, exactement n+2 facteurs de longueur n. Nous définissons également la notion d'insertion k à k sur les mots infinis puis nous calculons la complexité des mots obtenus en appliquant cette notion aux mots sturmiens. Enfin nous étudions l'équilibre et la palindromie d'une classe particulière de mots de complexité n+2 que nous appelons mots quasi-sturmiens...
Le but de cet article est de proposer une nouvelle méthode pour des études dans le cadre de la théorie des “dessins d’enfants” de A. Grothendieck de certaines questions concernant l’action du groupe de Galois absolu sur l’ensemble des arbres planaires.On définit l’application qui associe à chaque arbre planaire à arêtes, une courbe hyperelliptique avec un point de -division. Cette construction permet d’établir un lien entre la théorie de la torsion des courbes hyperelliptiques et celle des “dessins...
Ces notes ont pour but de rassembler les différents résultats de combinatoire des mots relatifs au billard polygonal et polyédral. On commence par rappeler quelques notions de combinatoire, puis on définit le billard, les notions utiles en dynamique et le codage de l’application. On énonce alors les résultats connus en dimension deux puis trois.
We study some arithmetical and combinatorial properties of
β-integers for β being the larger root of the equation
x2 = mx - n,m,n ∈ ℵ, m ≥ n +2 ≥ 3. We determine with
the accuracy of ± 1 the maximal number of β-fractional
positions, which may arise as a result of addition of two
β-integers. For the infinite word uβ> coding distances
between the consecutive β-integers, we determine precisely
also the balance. The word uβ> is the only fixed point of the
morphism A → Am-1B and B → Am-n-1B. In...
We use combinatorics to describe the topology of a singular irreducible plane curve germ f = 0 under small perturbation of parameters.
We provide combinatorial interpretations for three new classes of partitions, the so-called chromatic partitions. Using only combinatorial arguments, we show that these partition identities resemble well-know ordinary partition identities.
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