Results 111 to 120 of about 9,659,868 (257)
Special Matrices, 2020 In this paper, our main attention is paid to calculate the determinants and inverses of two types Toeplitz and Hankel tridiagonal matrices with perturbed columns.
Fu Yaru +3 more
doaj +1 more source
Investigation of Generalized Hybrid Fibonacci Numbers and Their Properties [PDF]
arXiv, 2018 In \cite{Oz}, M. \"Ozdemir defined a new non-commutative number system called hybrid numbers. In this paper, we define the hybrid Fibonacci and Lucas numbers. This number system can be accepted as a generalization of the complex ($\textbf{i}^{2}=-1$), hyperbolic ($\textbf{h}^{2}=1$) and dual Fibonacci number ($\varepsilon^{2}=0$) systems.
arxiv
ON THE GROUP OF THE FIBONACCI NUMBERS
, 2018 Here we will show that the numbers of Fibonacci are forming a group. Each number is represented by a 2x2 symmetric matrix and the operation of the group is the product of matrices. This approach allows to define the negaFibonacci numbers by means of the inverse of the Fibonacci matrices.
openaire +2 more sources
On Bicomplex Fibonacci Numbers and Their Generalization
, 2018 In this chapter, we consider bicomplex numbers with coefficients from Fibonacci sequence and give some identities. Moreover, we demonstrate the accuracy of such identities by taking advantage of idempotent representations of the bicomplex numbers. And then by this representation, we give some identities containing these numbers.
openaire +6 more sources
On Generalized Fibonacci Numbers [PDF]
The American Mathematical Monthly, 1971 (1971). On Generalized Fibonacci Numbers. The American Mathematical Monthly: Vol. 78, No. 10, pp. 1108-1109.
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On the sum of reciprocal generalized Fibonacci numbers [PDF]
arXiv, 2015 In this paper, we consider infinite sums derived from the reciprocals of the generalized Fibonacci numbers. We obtain some new and interesting identities for the generalized Fibonacci numbers.
arxiv
On the Frobenius Number of Fibonacci Numerical Semigroups [PDF]
, 2007 J. M. MARIN +2 more
openalex +1 more source
Hybrid Numbers with Fibonacci and Lucas Hybrid Number Coefficients [PDF]
, 2022 Emrah Polatlı
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Restricted Permutations, Fibonacci Numbers, and k-generalized Fibonacci Numbers
, 2005 In 1985 Simion and Schmidt showed that the number of permutations in Sn which avoid 132, 213, and 123 is equal to the Fibonacci number Fn+1. We use generating function and bijective techniques to give other sets of pattern-avoiding permutations which can be enumerated in terms of Fibonacci or k-generalized Fibonacci numbers.
Egge, Eric C., Mansour, Toufik
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Four New Generalized Fibonacci Number Summation Identities [PDF]
arXiv, 2018 Two new generalized Fibonacci number summation identities are stated and proved, and two other new generalized Fibonacci number summation identities are derived from these, of which two special cases are already known in literature.
arxiv