Determinantal and Permanental Representation of Generalized Fibonacci Polynomials

TL;DR

This paper presents new determinantal and permanental matrix representations for generalized Fibonacci polynomials, extending known results for Fibonacci and Pell sequences using Hessenberg matrices.

Contribution

It introduces generalized matrix representations for these polynomials, broadening the understanding of their algebraic structure and connections to matrix theory.

Findings

Determinantal representations using Hessenberg matrices.

Permanental representations using Hessenberg matrices.

Generalization of known Fibonacci and Pell number representations.

Abstract

In this paper, we give some determinantal and permanental representations of Generalized Fibonacci Polynomials by using various Hessenberg matrices. These results are general form of determinantal and permanental representations of k sequences of the generalized order-k Fibonacci and Pell numbers.