Results 11 to 20 of about 185 (126)
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
doaj +3 more sources
On Fibonacci quaternion matrix [PDF]
Notes on Number Theory and Discrete Mathematics, 2021 In this study, we have defined Fibonacci quaternion matrix and investigated its powers. We have also derived some important and useful identities such as Cassini’s identity using this new matrix.
Serpil Halici, Ömür Deveci
openaire +4 more sources
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
doaj +2 more sources
On quaternion-Gaussian Fibonacci polynomials
Miskolc Mathematical Notes, 2023 Summary: In this paper, we define Gaussian Fibonacci quaternion polynomials and Gaussian Lucas quaternion polynomials. We also investigate some properties of these quaternion polynomials.
Yağmur, Tülay
openaire +4 more sources
On the Periods of 2-Step General Fibonacci Sequences in the Generalized Quaternion Groups [PDF]
Discrete Dynamics in Nature and Society, 2012 We study 2-step general Fibonacci sequences in the generalized quaternion groups Q4n. In cases where the sequences are proved to be simply periodic, we obtain the periods of 2-step general Fibonacci sequences.
Bahram Ahmadi, Hossein Doostie
doaj +2 more sources
Unrestricted Fibonacci and Lucas quaternions
Fundamental Journal of Mathematics and Applications, 2021 Many quaternion numbers associated with Fibonacci and Lucas numbers or even their generalizations have been defined and widely discussed so far. In all the studies, the coefficients of these quaternions have been selected from consecutive terms of these numbers.
Ahmet DAŞDEMİR, Göksal BİLGİCİ
core +5 more sources
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
doaj +2 more sources
On the 2k-step Jordan-Fibonacci sequence
Advances in Difference Equations, 2017 In this paper, we define the 2k-step Jordan-Fibonacci sequence, and then we study the 2k-step Jordan-Fibonacci sequence modulo m. Also, we obtain the cyclic groups from the multiplicative orders of the generating matrix of the 2k-step Jordan-Fibonacci ...
Omur Deveci, Sait Taş, A Kılıçman
doaj +2 more sources
On circulant matrices with Fibonacci quaternions [PDF]
Notes on Number Theory and Discrete MathematicsIn literature, there exist many papers that compute determinants and some kinds of norms of circulant matrices involving some well-known number sequences.
Seda Yamaç Akbıyık +3 more
doaj +3 more sources
More Identities for Fibonacci and Lucas quaternions [PDF]
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2019 Summary: In this paper, we define the associate matrix as \[ F= \left( \begin{matrix} 1+i+2j+3k & i+j+2k \\ i+j+2k & 1+j+k \end{matrix} \right). \] By the means of the matrix \(F\), we give several identities about Fibonacci and Lucas quaternions by matrix methods.
Irmak, Nurettin
openaire +6 more sources