Related papers: Fibonacci vector and matrix p-norms
In this paper, we derive nearly tight probabilistic norm bounds for a class of random matrices we call graph matrices. While the classical case of symmetric matrices with independent random entries (Wigner's matrices) is a special case, in…
We consider $m$-th order linear recurrences that can be thought of as generalizations of the Lucas sequence. We exploit some interplay with matrices that again can be considered generalizations of the Fibonacci matrix. We introduce the…
A thorough analysis is made of the Fourier coefficients for vector-valued modular forms associated to three-dimensional irreducible representations of the modular group. In particular, the following statement is verified for all but a…
We study characteristic polynomials of symmetric matrices with entries ${i+j\choose i}$ the binomial coefficients, over finite fields.
Let $k\geq2$. Then the $k$-th order Fibonacci cube $\Gamma^{(k)}_{n}$ is the subgraph of the hypercube $Q_{n}$ induced by vertices without $k$ consecutive $1$s. The case $k=2$ corresponds to the classic Fibonacci cube $\Gamma_{n}$. There…
Symmetry is an important factor in solving many constraint satisfaction problems. One common type of symmetry is when we have symmetric values. In a recent series of papers, we have studied methods to break value symmetries. Our results…
In this paper we state some conjectures about q-Fibonacci polynomials which for q=1 reduce to well-known results about Fibonacci numbers and Fibonacci polynomials.
A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterised as those permutations not involving a particular set of forbidden permutations. A simple collection of necessary and…
Several classes of systems of evolution equations with one or two vector unknowns are considered. We investigate also systems with one vector and one scalar unknown. For these classes all equations having the simplest higher symmetry are…
The convolved Fibonacci numbers F_j^(r) are defined by (1-z-z^2)^{-r}=\sum_{j>=0}F_{j+1}^(r)z^j. In this note some related numbers that can be expressed in terms of convolved Fibonacci numbers are considered. These numbers appear in the…
The following article summarizes research where theorems and their respective demonstrations are postulated based on quadratic equations with special properties given by the Pythagorean triplets and the Fibonacci sequence given the second…
Matrix pencils, or pairs of matrices, may be used in a variety of applications. In particular, a pair of matrices (E,A) may be interpreted as the differential equation E x' + A x = 0. Such an equation is invariant by changes of variables,…
We prove geometric and scaling results for the real Fibonacci parameter value in the quadratic family $f_c(z) = z^2+c$. The principal nest of the Yoccoz parapuzzle pieces has rescaled asymptotic geometry equal to the filled-in Julia set of…
In this paper,we studied some properties of the Fibonacci map and find a property of this map related to the notation of principal nest. And weproved this property with some additional conditions equals the original definition of Fibonacci…
A full characterization of $(p,q)$-deformed Fibonacci and Lucas polynomials is given. These polynomials obey non-conventional three-term recursion relations. Their generating functions and Fourier integral transforms are explicitly computed…
Let (E,D,P) be a flat vector bundle with a parabolic structure over a punctured Riemann surface, (M,g). We consider a deformation of the harmonic metric equation which we call the Poisson metric equation. This equation arises naturally as…
In the present paper we propose generalizations of the regularity and counting lemmas for multidimensional matrices under a finite alphabet. Firstly, we prove a variant of a multidimensional regularity lemma with the help of a translation…
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 standard definition of the dimension of a vector space or rank of a module states that dimension or rank is equal to the cardinality of any basis, which requires an understanding of the concepts of basis, generating set, and linear…
We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.