Relevant bibliographies by topics / Fibonacci tiling

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Fibonacci tiling'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Fibonacci tiling"

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Lifshitz, Ron. "The square Fibonacci tiling." Journal of Alloys and Compounds 342, no. 1-2 (2002): 186–90. http://dx.doi.org/10.1016/s0925-8388(02)00169-x.

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TAŞYURDU, Yasemin, and Berke CENGİZ. "A TILING APPROACH TO FIBONACCI p-NUMBERS." Journal of Universal Mathematics 5, no. 2 (2022): 177–84. http://dx.doi.org/10.33773/jum.1142766.

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In this paper, we introduce tiling representations of Fibonacci p-numbers, which are generalizations of the well-known Fibonacci and Narayana numbers, and generalized in the distance sense. We obtain Fibonacci p-numbers count the number of distinct ways to tile a 1 × n board using various 1 × r, r-ominoes from r = 1 up to r = p + 1. Moreover, the product identities and sum formulas of these numbers with special subscripts are given by tiling interpretations that allow the derivation of their properties.
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Margenstern, Maurice. "Fibonacci Type Coding for the Regular Rectangular Tilings of the Hyperbolic Plane." JUCS - Journal of Universal Computer Science 9, no. (5) (2003): 398–422. https://doi.org/10.3217/jucs-009-05-0398.

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The study of cellular automata (CA) on tilings of hyperbolic plane was initiated in [6]. Appropriate tools were developed which allow us to produce linear algorithms to implement cellular automata on the tiling of the hyperbolic plane with the regular rectangular pentagons, [8, 10]. In this paper we modify and improve these tools, generalise the algorithms and develop them for tilings of the hyperbolic plane with regular rectangular s-gons for s 5. For this purpose a combinatorial structure of these tilings is studied.
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Huegy, Charles W., and Douglas B. West. "A Fibonacci tiling of the plane." Discrete Mathematics 249, no. 1-3 (2002): 111–16. http://dx.doi.org/10.1016/s0012-365x(01)00239-4.

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Tasyurdu, Yasemin. "Generalized Fibonacci numbers with five parameters." Thermal Science 26, Spec. issue 2 (2022): 495–505. http://dx.doi.org/10.2298/tsci22s2495t.

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In this paper, we define five parameters generalization of Fibonacci numbers that generalizes Fibonacci, Pell, Modified Pell, Jacobsthal, Narayana, Padovan, k-Fibonacci, k-Pell, Modified k-Pell, k-Jacobsthal numbers and Fibonacci p-numbers, distance Fibonacci numbers, (2, k)-distance Fibonacci numbers, generalized (k, r)-Fibonacci numbers in the distance sense by extending the definition of a distance in the recurrence relation with two parameters and adding three parameters in the definition of this distance, simultaneously. Tiling and combinatorial interpretations of generalized Fibonacci nu
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Amaral, Marcelo, David Chester, Fang Fang, and Klee Irwin. "Exploiting Anyonic Behavior of Quasicrystals for Topological Quantum Computing." Symmetry 14, no. 9 (2022): 1780. http://dx.doi.org/10.3390/sym14091780.

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The concrete realization of topological quantum computing using low-dimensional quasiparticles, known as anyons, remains one of the important challenges of quantum computing. A topological quantum computing platform promises to deliver more robust qubits with additional hardware-level protection against errors that could lead to the desired large-scale quantum computation. We propose quasicrystal materials as such a natural platform and show that they exhibit anyonic behavior that can be used for topological quantum computing. Different from anyons, quasicrystals are already implemented in lab
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Artz, Jacob, and Michael Rowell. "A tiling approach to Fibonacci product identities." Involve, a Journal of Mathematics 2, no. 5 (2010): 581–87. http://dx.doi.org/10.2140/involve.2009.2.581.

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8

Gähler, F., and E. Miro. "Topology of the Random Fibonacci Tiling Space." Acta Physica Polonica A 126, no. 2 (2014): 564–67. http://dx.doi.org/10.12693/aphyspola.126.564.

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BERKOFF, A. M., J. M. HENLE, A. E. MCDONOUGH, and A. P. WESOLOWSKI. "POSSIBILITIES AND IMPOSSIBILITIES IN SQUARE-TILING." International Journal of Computational Geometry & Applications 21, no. 05 (2011): 545–58. http://dx.doi.org/10.1142/s0218195911003792.

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A set of natural numbers tiles the plane if a square-tiling of the plane exists using exactly one square of sidelength n for every n in the set. From Ref. 8 we know that ℕ itself tiles the plane. From that and Ref. 9 we know that the set of even numbers tiles the plane while the set of odd numbers doesn't. In this paper we explore the nature of this property. We show, for example, that neither tiling nor non-tiling is preserved by superset. We show that a set with one or three odd numbers may tile the plane—but a set with two odd numbers can't. We find examples of both tiling and non-tiling se
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10

BEN-ABRAHAM, S. I. "DEFECTIVE VERTEX CONFIGURATIONS IN QUASICRYSTALLINE STRUCTURES." International Journal of Modern Physics B 07, no. 06n07 (1993): 1415–25. http://dx.doi.org/10.1142/s0217979293002407.

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Defective vertex configurations are important for the whole range of models for quasicrystalline structures from quasiperiodic tilings through random tilings to polyhedral glasses. The combinatorially possible vertex configurations are enumerated for the 1D Fibonacci chain, for the 2D Penrose pattern with its generalizations, as well as for the Beenker pattern and the triangle pattern, and for the 3D simple icosahedral tiling. The methods for quantifying the deviation of vertex configurations from perfection are reviewed. The simple method of partial dual overlap provides a means to estimate t
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Dissertations / Theses on the topic "Fibonacci tiling"

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Spreafico, Elen Viviani Pereira 1986. "Novas identidades envolvendo os números de Fibonacci, Lucas e Jacobsthal via ladrilhamentos." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307509.

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Orientador: José Plínio de Oliveira Santos<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-26T02:14:38Z (GMT). No. of bitstreams: 1 Spreafico_ElenVivianiPereira_D.pdf: 1192138 bytes, checksum: 2b12cd351b94a0f2f7ec24fc172305c9 (MD5) Previous issue date: 2014<br>Resumo: Neste trabalho, colaboramos com provas combinatórias que utilizam a contagem e a q-contagem de elementos em conjuntos de ladrilhamentos com restrições. Na primeira parte do trabalho utilizamos os ladrilhamentos para demo
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Thiem, Stefanie. "Electronic and Photonic Properties of Metallic-Mean Quasiperiodic Systems." Doctoral thesis, Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-83831.

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Understanding the connection of the atomic structure and the physical properties of materials remains one of the elementary questions of condensed-matter physics. One research line in this quest started with the discovery of quasicrystals by Shechtman et al. in 1982. It soon became clear that these materials with their 5-, 8-, 10- or 12-fold rotational symmetries, which are forbidden according to classical crystallography, can be described in terms of mathematical models for nonperiodic tilings of a plane proposed by Penrose and Ammann in the 1970s. Due to the missing translational symmetry of
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Thiem, Stefanie. "Electronic and Photonic Properties of Metallic-Mean Quasiperiodic Systems." Doctoral thesis, 2011. https://monarch.qucosa.de/id/qucosa%3A19673.

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Understanding the connection of the atomic structure and the physical properties of materials remains one of the elementary questions of condensed-matter physics. One research line in this quest started with the discovery of quasicrystals by Shechtman et al. in 1982. It soon became clear that these materials with their 5-, 8-, 10- or 12-fold rotational symmetries, which are forbidden according to classical crystallography, can be described in terms of mathematical models for nonperiodic tilings of a plane proposed by Penrose and Ammann in the 1970s. Due to the missing translational symmetry o
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Book chapters on the topic "Fibonacci tiling"

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Hare, E. O., and P. Z. Chinn. "Tiling with Cuisenaire Rods." In Applications of Fibonacci Numbers. Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-009-0223-7_15.

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"Bivariate Tiling Models." In Fibonacci and Lucas Numbers With Applications. John Wiley & Sons, Inc., 2019. http://dx.doi.org/10.1002/9781118742297.ch46.

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"Chebyshev Tilings." In Fibonacci and Lucas Numbers With Applications. John Wiley & Sons, Inc., 2019. http://dx.doi.org/10.1002/9781118742297.ch42.

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"PENROSE TILINGS." In The Golden Ratio and Fibonacci Numbers. WORLD SCIENTIFIC, 1997. http://dx.doi.org/10.1142/9789812386304_0011.

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"Jacobsthal Tilings and Graphs." In Fibonacci and Lucas Numbers With Applications. John Wiley & Sons, Inc., 2019. http://dx.doi.org/10.1002/9781118742297.ch45.

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"Tilings: Divisibility Properties of the Fibonacci Numbers." In Fibonacci and Catalan Numbers. John Wiley & Sons, Inc., 2011. http://dx.doi.org/10.1002/9781118159743.ch7.

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Conference papers on the topic "Fibonacci tiling"

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Kazlacheva, Zlatina, and Irina Ruseva. "A study on applying of golden ratio and Fibonacci sequence tilings in sustainable fashion design and pattern making." In WORLD MULTIDISCIPLINARY CIVIL ENGINEERING-ARCHITECTURE-URBAN PLANNING SYMPOSIUM WMCAUS 2022. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0172808.

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You might also be interested in the extended bibliographies on the topic 'Fibonacci tiling' for particular source types:
Journal articles
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