Determinantal and permanental representation of generalized bivariate Fibonacci p-polynomials

TL;DR

This paper presents determinantal and permanental matrix representations for generalized bivariate Fibonacci p-polynomials, unifying various polynomial families like Fibonacci, Pell, and Chebyshev through Hessenberg matrices.

Contribution

It introduces new matrix-based representations for generalized bivariate Fibonacci p-polynomials, encompassing many classical polynomial families.

Findings

Derived determinantal representations using Hessenberg matrices.

Established permanental representations for the polynomials.

Unified various polynomial families under a common matrix framework.

Abstract

In this paper, we give some determinantal and permanental representations of generalized bivariate Fibonacci p-polynomials by using various Hessenberg matrices. The results that we obtained are important since generalized bivariate Fibonacci p-polynomials are general form of, for example, bivariate Fibonacci and Pell p-polynomials, second kind Chebyshev polynomials, bivariate Jacobsthal polynomials etc.