Related papers: Fibonacci Chain Polynomials: Identities from Self-…
Among the classical models for interconnection networks are hypercubes and Fibonacci cubes. Fibonacci cubes are induced subgraphs of hypercubes obtained by restricting the vertex set to those binary strings which do not contain consecutive…
A filter lattice is a distributive lattice formed by all filters of a poset in the anti-inclusion order. We study the combinatorial properties of the Hasse diagrams of filter lattices of certain posets, so called Fibonacci-like cubes, in…
In this paper, we connect two well established theories, the Fibonacci numbers and the Jordan algebras. We give a series of matrices, from literature, used to obtain recurrence relations of second-order and polynomial sequences. We also…
In this short note, we establish some identities containing sums of binomials with coefficients satisfying third order linear recursive relations. As a result and in particular, we obtain general forms of earlier identities involving…
We derive a general recurrence relation for squares of Fibonacci-like numbers. Various properties are developed, including double binomial summation identites.
The Fibonacci cube $\Gamma_n$ is the subgraph of the hypercube $Q_n$ induced by vertices with no consecutive $1$s. Recently Jianxin Wei and Yujun Yang introduced a one parameter generalization, Fibonacci $p$-cubes $\Gamma_n^p$, which are…
We look at a family of meta-Fibonacci sequences which arise in studying the number of leaves at the largest level in certain infinite sequences of binary trees, restricted compositions of an integer, and binary compact codes. For this…
In this paper, we define the bi-periodic Fibonacci matrix sequence that represent bi-periodic Fibonacci numbers. Then, we investigate generating function, Binet formula and summations of bi-periodic Fibonacci matrix sequence. After that, we…
We afford the problem of counting the blocks of a given length made with symbols drawn from an alphabet and relate this number to Fibonacci-like recurrent relations. The recurrence polynomia allows to calculate the limit ratio of two…
Let $p$ be a prime. In this paper, we give a complete classification of self-reciprocal polynomials arising from Fibonacci polynomials over $\mathbb{Z}$ and $\mathbb{Z}_p$, where $p=2$ and $p>5$. We also present some partial results when…
Fibonacci cubes are induced subgraphs of hypercube graphs obtained by restricting the vertex set to those binary strings which do not contain consecutive 1s. This class of graphs has been studied extensively and generalized in many…
We study the random Fibonacci tree, which is an infinite binary tree with non-negative integers at each node. The root consists of the number 1 with a single child, also the number 1. We define the tree recursively in the following way: if…
This paper describes a class of sequences that are in many ways similar to Fibonacci sequences: given n, sum the previous two terms and divide them by the largest possible power of n. The behavior of such sequences depends on n. We analyze…
The study describes a class of integer labelings of the Fibonacci tree, the tree of descent introduced by Fibonacci. In these labelings, Fibonacci sequences appear along ascending branches of the tree, and it is shown that the labels at any…
The Fibonacci numbers are a sequence of integers in which every number after the first two, 0 and 1, is the sum of the two preceding numbers. These numbers are well known and algorithms to compute them are so easy that they are often used…
Double Fibonacci sequences are introduced and they are related to operations with Fibonacci modules. Generalizations and examples are also discussed.
In this study, the new algebraic properties related to bivariate Fibonacci polynomials has been given. We present the partial derivatives of these polynomials in the form of convolution of bivariate Fibonacci polynomials. Also, we define a…
We consider four masses in a circular configuration with nearest-neighbour interaction, generalizing the spatially periodic Fermi--Pasta--Ulam-chain where all masses are equal. We identify the mass ratios that produce the…
Protein-fragment seqlets typically feature about 10 amino acid residue positions that are fixed to within conservative substitutions but usually separated by a number of prescribed gaps with arbitrary residue content. By quantifying a…
The inhomogeneous Fermi-Pasta-Ulam chain is studied by identifying the mass ratios that produce prominent resonances. This is a technically complicated problem as we have to solve an inverse problem for the spectrum of the corresponding…