Related papers: Fibonacci-Lucas Spinors Obtained from Hybrid Numbe…
One of the most popular and studied recursive series is the Fibonacci sequence. It is challenging to see how Fibonacci numbers can be used to generate other recursive sequences. In our article, we describe some families of integer…
Using elementary methods, we establish old and new relations between binomial coefficients, Fibonacci numbers, Lucas numbers, and more.
We give an explicit bijective correspondence between between nonzero pairs of complex numbers, which we regard as spinors or spin vectors, and horospheres in 3-dimensional hyperbolic space decorated with certain spinorial directions. This…
We evaluate binomial series with harmonic number coefficients, providing recursion relations, integral representations, and several examples. The results are of interest to analytic number theory, the analysis of algorithms, and…
The Lucas sequences are integers defined by a homogeneous recurrence relation. They include the well-known Fibonacci numbers, which appear abundantly in nature. The complementary Lucas numbers, defined by the same recurrence relation, are…
Double Fibonacci sequences are introduced and they are related to operations with Fibonacci modules. Generalizations and examples are also discussed.
The Fibonacci sequence is a sequence of numbers that has been studied for hundreds of years. In this paper, we introduce the new sequence S_{k,n} with initial conditions S_{k,0} = 2b and S_{k,1} = bk + a, which is generated by the…
A beautiful theorem of Thomas Price links the Fibonacci numbers and the Lucas polynomials to the plane geometry of an ellipse, generalizing a classic problem about circles. We give a brief history of the circle problem, an account of…
We give explicit bijective correspondences between three families of objects: certain pairs of quaternions, which we regard as spinors; certain flags in (1+4)-dimensional Minkowski space; and horospheres in 4-dimensional hyperbolic space…
I begin by explaining how Riemannian geometry can be understood in terms of principal fibre bundles and connections thereon. I then introduce and motivate the definition of a spinor structure in terms of familiar geometrical ideas. The…
Let $(F_n)_{n\geq 0}$ and $(L_n)_{n\geq 0}$ be the Fibonacci and Lucas sequences, respectively. In this paper we determine all Fibonacci numbers which are mixed concatenations of a Fibonacci and a Lucas numbers. By mixed concatenations of $…
By using definition of Golden derivative, corresponding Golden exponential function and Fibonomial coefficients, we introduce generating functions for Bernoulli-Fibonacci polynomials and related numbers. Properties of these polynomials and…
The objective of this manuscript is to offer explicit expressions for diverse categories of infinite series incorporating the Fibonacci (Lucas) sequence and the Riemann zeta function. In demonstrating our findings, we will utilize…
In this paper, we present a new approach to the convolved Fibonacci numbers arising from the generating function of them and give some new and explicit identities for the convolved Fibonacci numbers.
The spinorial degrees of freedom of two or more spacelike separated Dirac particles are considered and a method for constructing mixed polynomials that are invariant under the spinor representations of the local proper orthochronous Lorentz…
At this paper, we derive some relationships between permanents of one type of lower-Hessenberg matrix and the Fibonacci and Lucas numbers and their sums.
In this paper, new families of generalized Fibonacci and Lucas numbers are introduced. In addition, we present the recurrence relations and the generating functions of the new families for $k=2$.
The purpose of this paper is to investigate integer sequences with exponent lifting property, a property common in Fibonacci or Lucas sequences.
We formulate Lorentz group representations in which ordinary complex numbers are replaced by linear functions of real quaternions and introduce dotted and undotted quaternionic one-dimensional spinors. To extend to parity the space-time…
Spivey presented a new approach to evaluate combinatorial sums by using finite differences. We present some closed forms for sums involving the binomial coefficients, Fibonacci and Lucas numbers in terms of the falling factorial.