Results 1 to 10 of about 69,814 (147)
The quaternion-type cyclic-Fibonacci sequences in groups [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we define the six different quaternion-type cyclic-Fibonacci sequences and present some properties, such as, the Cassini formula and generating function. Then, we study quaternion-type cyclic-Fibonacci sequences modulo m.
Nazmiye Yilmaz +2 more
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Some Identities of Fibonacci and Lucas Quaternions by Quaternion Matrices [PDF]
Düzce Üniversitesi Bilim ve Teknoloji Dergisi, 2019 In this paper, we consider one of the most knownFibonacci matrix Qand the Fibonacciquaternion matrix MQFn, where Qnis the n-th Fibonacci quaternion.In particular we define some new quaternion matrices.
Bahar Demirtürk Bitim
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Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers
Journal of Mathematics, 2023 In this paper, we define a new sequence called the quaternion-type Catalan sequence and give generating function, exponential representation, quaternionic Catalan matrix and its some properties.
Kübra Gül
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On Quaternion Gaussian Bronze Fibonacci Numbers
Annales Mathematicae Silesianae, 2022 In the present work, a new sequence of quaternions related to the Gaussian Bronze numbers is defined and studied. Binet’s formula, generating function and certain properties and identities are provided.
Catarino Paula, Ricardo Sandra
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Binomial transform of the bivariate Fibonacci quaternion polynomials and its properties [PDF]
Notes on Number Theory and Discrete MathematicsThe primary aim of this work is to deal with binomial transforms of bivariate Fibonacci quaternion polynomial sequence. The binomial sequence of the bivariate Fibonacci quaternion polynomial is found, and then results are obtained for the recurrence ...
Faruk Kaplan, Arzu Özkoç Öztürk
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On Quaternion-Gaussian Fibonacci Numbers and Their Properties
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 We study properties of Gaussian Fibonacci numbers. We start with some basic identities. Thereafter, we focus on properties of the quaternions that accept gaussian Fibonacci numbers as coefficients.
Halici Serpil, Cerda-Morales Gamaliel
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Construction of dual-generalized complex Fibonacci and Lucas quaternions
Karpatsʹkì Matematičnì Publìkacìï, 2022 The aim of this paper is to construct dual-generalized complex Fibonacci and Lucas quaternions. It examines the properties both as dual-generalized complex number and as quaternion. Additionally, general recurrence relations, Binet's formulas, Tagiuri's (
G.Y. Şentürk, N. Gürses, S. Yüce
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A quantum calculus framework for Gaussian Fibonacci and Gaussian Lucas quaternion numbers [PDF]
Notes on Number Theory and Discrete MathematicsIn order to investigate the relationship between Gaussian Fibonacci numbers and quantum numbers and to develop both a deeper theoretical understanding in this study, q-Gaussian Fibonacci, q-Gaussian Lucas quaternions and polynomials are taken with ...
Bahar Kuloğlu
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Pauli Gaussian Fibonacci and Pauli Gaussian Lucas Quaternions
Mathematics, 2022 We have investigated new Pauli Fibonacci and Pauli Lucas quaternions by taking the components of these quaternions as Gaussian Fibonacci and Gaussian Lucas numbers, respectively. We have calculated some basic identities for these quaternions.
Ayse Zeynep Azak
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New summation identities of hyperbolic k-Fibonacci and k-Lucas quaternions [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, we introduce a set of identities involving hyperbolic k-Fibonacci quaternions and k-Lucas quaternions. Moreover, we derive summation identities for hyperbolic k-Fibonacci and k-Lucas quaternions by utilizing established properties of k ...
A. D. Godase
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