The generalized Lucas hybrinomials with two variables

On generalized Lucas sequences

We introduce the notions of unsigned and signed generalized Lucas sequences and prove certain polynomial recurrence relations on their characteristic polynomials. We also characterize when these characteristic polynomials are irreducible polynomials over a finite field. Moreover, we obtain the explicit expressions of the remainders of Dickson polynomials of the first kind divided by the charact...

Generalized Lucas cubes

Let f be a binary string and d C 1. Then the generalized Lucas cube Qd(JÐf ) is introduced as the graph obtained from the d-cube Qd by removing all vertices that have a circulation containing f as a substring. The question for which f and d, the generalized Lucas cube Qd(JÐf ) is an isometric subgraph of the d-cube Qd is solved for all binary strings of length at most five. Several isometricall...

On the order-k generalized Lucas numbers

In this paper we give a new generalization of the Lucas numbers in matrix representation. Also we present a relation between the generalized order-k Lucas sequences and Fibonacci sequences. 2003 Elsevier Inc. All rights reserved.

On a Generalized Retarded Integral Inequality with Two Variables

Determinants and permanents of Hessenberg matrices and generalized Lucas polynomials

In this paper, we give some determinantal and permanental representations of generalized Lucas polynomials, which are a general form of generalized bivariate Lucas p-polynomials, ordinary Lucas and Perrin sequences etc., by using various Hessenberg matrices. In addition, we show that determinant and permanent of these Hessenberg matrices can be obtained by using combinations. Then we show, the ...