We show that there are relationships between a generalized Lucas sequence and the permanent and determinant of some Hessenberg matrices.

in this study, a new and ecient approach is presented for numerical solution offredholm integro-dierential equations (fides) of the second kind on unbounded domainwith degenerate kernel based on operational matrices with respect to generalized laguerrepolynomials(glps). properties of these polynomials and operational matrices of integration,dierentiation are introduced and are ultilized to r...

Generalized polynomials are defined as products of polynomials raised to positive real powers. The generalized degree can be defined in a natural way. A number of classical inequalities holding for polynomials can be extended for generalized polynomials utilizing the generalized degree in place of the ordinary one. Remez established a sharp upper bound for the maximum modulus on [— 1,1] of alge...

We develop polynomials in z ∈ C for which some generalized harmonic numbers are special cases at z= 0. By using the Riordan array method, we explore interesting relationships between these polynomials, the generalized Stirling polynomials, the Bernoulli polynomials, the Cauchy polynomials and the Nörlund polynomials. © 2007 Elsevier B.V. All rights reserved.

In this paper, we consider the relationships between the sums of the generalized order-k Fibonacci and Lucas numbers and 1-factors of bipartite graphs. 1. Introduction We consider the generalized order k Fibonacci and Lucas numbers. In [1], Er de…ned k sequences of the generalized order k Fibonacci numbers as shown: g n = k X j=1 g n j ; for n > 0 and 1 i k; (1.1) with boundary conditions for 1...

We introduce a new statistic on linear and circular r-mino arrangements which leads to interesting polynomial generalizations of the r-Fibonacci and r-Lucas sequences. By studying special values of these polynomials, we derive periodicity and parity theorems for this statistic.

Wythoff s game is a variation of Nim, a two-pile game in which each player removes counters in turn until the winner takes the last counter. The safe-pairs generated in the solution of Wythoff's game have many properties interesting in themselves, and are related to the canonical Zeckendorf representation of an integer using Fibonacci numbers. In Nim, the strategy is related to expressing the n...