Fibonacci cubes, extended Fibonacci cubes, and Lucas cubes are induced subgraphs of hypercubes 9 defined in terms of Fibonacci strings. It is shown that all these graphs are median. Several enumeration results on the number of their edges and squares are obtained. Some identities involving Fibonacci 11 and Lucas numbers are also presented. © 2005 Published by Elsevier B.V. 13

We introduce the concept of D-operators associated to a sequence of polynomials (pn)n and an algebra A of operators acting in the linear space of polynomials. In this paper, we show that this concept is a powerful tool to generate families of orthogonal polynomials which are eigenfunctions of a higher order difference or differential operator. Indeed, given a classical discrete family (pn)n of ...

Motivation: Computations with algebraic numbers are of key importance in several geometric computations. Algebraic numbers arise as solutions to systems of polynomials—a common operation in many geometric applications, particularly those involving curved objects. Polynomials regularly describe the relationships between even basic geometric objects, for example the (squared) distance between two...

The main goal of the present paper is to construct some families of the Carlitz's $q$-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz's $q$-Bernoulli polynomials and numbers with weight ($_{p}$. We then define the modified degenerate Carlitz's $q$-Bernoulli polynomials and numbers with weight ($alpha ,beta $) and obtain some recurrence relations and other identities...

from the early 1950s, estimating the autocorrelations of polynomials with coefficients on the unit circle has found applications in ising spin systems and in surface acoustic wave designs. in this paper, a technique is introduced that not only estimates the autocorrelations, but for some special types of such polynomials, it locates the frequencies at which maximum autocorrelation occurs.

let g = (v, e) be a simple graph. hosoya polynomial of g isd(u,v)h(g, x) = {u,v}v(g)x , where, d(u ,v) denotes the distance between vertices uand v. as is the case with other graph polynomials, such as chromatic, independence anddomination polynomial, it is natural to study the roots of hosoya polynomial of a graph. inthis paper we study the roots of hosoya polynomials of some specific graphs.

In this work we give an alterative proof of one of basic properties of zonal polynomials and generalised it for Jack polynomials

Tribonacci polynomial sequence is an extension of numbers. We consider integer enumerating the number subsets S set [n]={1,2, . ,n } containing no three consecutive even integers. define a generalizing this sequence. The associated with polynomials. find closed form formula and derive some basic properties

In this paper, we …nd families of (0; 1; 1) tridiagonal matrices whose determinants and permanents equal to the negatively subscripted Fibonacci and Lucas numbers. Also we give complex factorizations of these numbers by the …rst and second kinds of Chebyshev polynomials. 1. Introduction The well-known Fibonacci sequence, fFng ; is de…ned by the recurrence relation, for n 2 Fn+1 = Fn + Fn 1 (1.1...