Results 21 to 30 of about 3,045 (188)
Fibonacci Identities via Fibonacci Functions
, 2023 We present a differential-calculus-based method which allows one to derive more identities from {\it any} given Fibonacci-Lucas identity containing a finite number of terms and having at least one free index. The method has two {\it independent} components.
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The complex-type cyclic-Fibonacci sequence and its applications [PDF]
Journal of Mahani Mathematical Research, 2023 In the present paper, we aim to generalize the notion of complex-type Fibonacci sequences to complex-type cyclic Fibonacci sequences. Firstly, we define the complex-type cyclic-Fibonacci sequence and then we give miscellaneous properties of this ...
Ömür Deveci +2 more
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Counting Maximal Distance-Independent Sets in Grid Graphs
Discussiones Mathematicae Graph Theory, 2013 Previous work on counting maximal independent sets for paths and certain 2-dimensional grids is extended in two directions: 3-dimensional grid graphs are included and, for some/any ℓ ∈ N, maximal distance-ℓ independent (or simply: maximal ℓ-independent ...
Euler Reinhardt +2 more
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The phyllotaxis of the aortic valve
Monaldi Archives for Chest Disease, 2019 Biological systems ubiquitously and inevitably exhibit stochasticity in traits from the molecular level to the multicellular and morphological level.
Marco Moscarelli, Ruggero De Paulis
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Novel Fibonacci and non-Fibonacci structure in the sunflower: results of a citizen science experiment [PDF]
Royal Society Open Science, 2016 This citizen science study evaluates the occurrence of Fibonacci structure in the spirals of sunflower (Helianthus annuus) seedheads. This phenomenon has competing biomathematical explanations, and our core premise is that observation of both Fibonacci ...
Jonathan Swinton, Erinma Ochu,
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On the Inverse of a Fibonacci Number Modulo a Fibonacci Number Being a Fibonacci Number
Mediterranean Journal of Mathematics, 2023 Let $(F_n)_{n \geq 1}$ be the sequence of Fibonacci numbers. For all integers $a$ and $b \geq 1$ with $\gcd(a, b) = 1$, let $[a^{-1} \!\bmod b]$ be the multiplicative inverse of $a$ modulo $b$, which we pick in the usual set of representatives $\{0, 1, \dots, b-1\}$. Put also $[a^{-1} \!\bmod b] := \infty$ when $\gcd(a, b) > 1$.
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Editorial: A note on Papal Mathematics [PDF]
Notes on Number Theory and Discrete MathematicsMany recent media claims that Pope Leo XIV, Robert F. Prevost, born in the USA and elected in 2025 in succession to Pope Francis, is the first mathematician to become the Pope of the Catholic Church are questionable. That honour probably belongs to Pope
Anthony G. Shannon
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Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023 In this paper, we define bi-periodic (p,q)-Fibonacci and bi-periodic (p,q)-Lucas sequences, which generalize Fibonacci type, Lucas type, bi-periodic Fibonacci type and bi-periodic Lucas type sequences, using recurrence relations of (p,q)-Fibonacci and (p,
Yasemin Taşyurdu +1 more
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Fibonacci Modules and Multiple Fibonacci Sequences
Ars Comb., 2008 Double Fibonacci sequences are introduced and they are related to operations with Fibonacci modules. Generalizations and examples are also discussed.
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The Fibonacci Dimension of a Graph [PDF]
The Electronic Journal of Combinatorics, 2011 The Fibonacci dimension ${\rm fdim}(G)$ of a graph $G$ is introduced as the smallest integer $f$ such that $G$ admits an isometric embedding into $\Gamma_f$, the $f$-dimensional Fibonacci cube. We give bounds on the Fibonacci dimension of a graph in terms of the isometric and lattice dimension, provide a combinatorial characterization of the Fibonacci
Cabello, Sergio +2 more
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