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Bibliografias temáticas / Nombres de Fibonacci

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Literatura científica selecionada sobre o tema "Nombres de Fibonacci"

Autor: Grafiati

Publicado: 7 de setembro de 2024

Última modificação: 31 de julho de 2025

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Artigos de revistas sobre o assunto "Nombres de Fibonacci"

1

FROUGNY, CHRISTIANE, та JACQUES SAKAROVITCH. "AUTOMATIC CONVERSION FROM FIBONACCI REPRESENTATION TO REPRESENTATION IN BASE φ, AND A GENERALIZATION". International Journal of Algebra and Computation 09, № 03n04 (1999): 351–84. http://dx.doi.org/10.1142/s0218196799000230.

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Every positive integer can be written as a sum of Fibonacci numbers; it can also be written as a (finite) sum of (positive and negative) powers of the golden mean φ. We show that there exists a letter-to-letter finite two-tape automaton that maps the Fibonacci representation of any positive integer onto its φ-expansion, provided the latter is folded around the radix point. As a corollary, the set of φ-expansions of the positive integers is a linear context-free language. These results are actually proved in the more general case of quadratic Pisot units. Résumé: Tout nombre entier positif peut

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2

Bugeaud, Yann, Maurice Mignotte, and Samir Siksek. "Sur les nombres de Fibonacci de la forme." Comptes Rendus Mathematique 339, no. 5 (2004): 327–30. http://dx.doi.org/10.1016/j.crma.2004.06.007.

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3

Belbachir, Hacène, and Assia Fettouma Tebtoub. "Les nombres de Stirling associés avec succession d'ordre 2, nombres de Fibonacci–Stirling et unimodalité." Comptes Rendus Mathematique 353, no. 9 (2015): 767–71. http://dx.doi.org/10.1016/j.crma.2015.06.008.

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4

RIVOAL, TANGUY. "ON THE BITS COUNTING FUNCTION OF REAL NUMBERS." Journal of the Australian Mathematical Society 85, no. 1 (2008): 95–111. http://dx.doi.org/10.1017/s1446788708000591.

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AbstractLet Bn(x) denote the number of 1’s occurring in the binary expansion of an irrational number x>0. A difficult problem is to provide nontrivial lower bounds for Bn(x) for interesting numbers such as $\sqrt {2}$, e or π: their conjectural simple normality in base 2 is equivalent to Bn(x)∼n/2. In this article, amongst other things, we prove inequalities relating Bn(x+y), Bn(xy) and Bn(1/x) to Bn(x) and Bn(y) for any irrational numbers x,y>0, which we prove to be sharp up to a multiplicative constant. As a by-product, we provide an answer to a question raised by Bailey et al. (D. H.

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5

Linton, Stephen, James Propp, Tom Roby, and Julian West. "Equivalence Relations of Permutations Generated by Constrained Transpositions." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AN,..., Proceedings (2010). http://dx.doi.org/10.46298/dmtcs.2841.

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International audience We consider a large family of equivalence relations on permutations in $S_n$ that generalise those discovered by Knuth in his study of the Robinson-Schensted correspondence. In our most general setting, two permutations are equivalent if one can be obtained from the other by a sequence of pattern-replacing moves of prescribed form; however, we limit our focus to patterns where two elements are transposed, conditional upon the presence of a third element of suitable value and location. For some relations of this type, we compute the number of equivalence classes, determin

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6

Battaglino, Daniela, Jean-Marc Fédou, Simone Rinaldi, and Samanta Socci. "The number of $k$-parallelogram polyominoes." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AS,..., Proceedings (2013). http://dx.doi.org/10.46298/dmtcs.2370.

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International audience A convex polyomino is $k$-$\textit{convex}$ if every pair of its cells can be connected by means of a $\textit{monotone path}$, internal to the polyomino, and having at most $k$ changes of direction. The number $k$-convex polyominoes of given semi-perimeter has been determined only for small values of $k$, precisely $k=1,2$. In this paper we consider the problem of enumerating a subclass of $k$-convex polyominoes, precisely the $k$-$\textit{convex parallelogram polyominoes}$ (briefly, $k$-$\textit{parallelogram polyominoes}$). For each $k \geq 1$, we give a recursive dec

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Teses / dissertações sobre o assunto "Nombres de Fibonacci"

1

Plet, Sébastien. "Mesures et densités des nombres premiers dans les suites récurrentes linéaires." Caen, 2006. http://www.theses.fr/2006CAEN2069.

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Nous donnons une construction générale d'espaces probabilisés sur [0,1], avec une mesure notée µ. Puis nous définirons cette mesure µ dans le cadre des groupes profinis, en particulier dans le cas où ces groupes profinis proviennent des groupes de Galois, définis sur des tours d'extensions galoisiennes de corps de nombres. Nous ferons apparaître ces tours d'extensions de corps en étudiant des propriétés liées à la divisibilité par des nombres premiers de termes de certaines suites récurrentes linéaires intégrales. Par exemple, nous allons démontrer les conjectures de Paul S. Bruckman et Peter

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2

Hong, Haojie. "Grands diviseurs premiers de suites récurrentes linéaires." Electronic Thesis or Diss., Bordeaux, 2024. http://www.theses.fr/2024BORD0107.

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Cette thèse porte sur les minorations des plus grands diviseurs premiers de suites récurrentes linéaires. Tout d’abord, nous obtenons une version uniforme et explicite du résultat séminal de Stewart sur les diviseurs premiers des suites de Lucas. Nous montrons que les constantes du théorème de Stewart ne dépendent que du corps quadratique correspondant à la suite de Lucas, mais pas d’autres paramètres. Nous étudions ensuite les diviseurs premiers des ordres de courbes elliptiques sur des corps finis. En fixant une courbe elliptique sur un corps fini Fq avec q puissance d’un nombre premier, la

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Livros sobre o assunto "Nombres de Fibonacci"

1

Fibonacci, El Somiador De Nombres. Editorial Juventud, S.A., 2011.

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2

Lines, Malcolm E. Dites un chiffre : Idées et problèmes mathématiques qui défient notre intelligence. Flammarion, 2002.

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Capítulos de livros sobre o assunto "Nombres de Fibonacci"

1

"FIBONACCI AND ARABIC MATHEMATICS." In Arithmétique, Algèbre et Théorie des Nombres. De Gruyter, 2023. http://dx.doi.org/10.1515/9783110784718-020.

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2

"FIBONACCI AND THE LATIN EXTENSION OF ARABIC MATHEMATICS." In Arithmétique, Algèbre et Théorie des Nombres. De Gruyter, 2023. http://dx.doi.org/10.1515/9783110784718-025.

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3

"Fibonacci et le nombre d’or." In Rencontres au pays des maths. EDP Sciences, 2023. http://dx.doi.org/10.1051/978-2-7598-3137-1.c029.

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4

"Fibonacci et le nombre d’or." In Rencontres au pays des maths. EDP Sciences, 2023. https://doi.org/10.1051/978-2-7598-3136-4.c029.

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