Some Remarks on Fibonacci-type Recursive Polynomials

Authors

Kristen Hallas, The University of Texas Rio Grande Valley
Joan Mattle
Deanna Perez
Aklilu Zeleke

Document Type

Conference Proceeding

Publication Date

7-16-2025

Abstract

We present properties of the classic Fibonacci-type recursive polynomials defined by Hoggatt in 1973 and the Golden-type recursive polynomials described by Moore in 1993. This work introduces a second order recursive sequence of Golden-like polynomials defined by Gn+1(x)=xkGn(x)+xlGn−1(x),k,lpositive integers

with G0=−1,G1=x−1

In this work, we explore some properties of this Golden-type polynomial sequence. We derive a Binet form for the polynomial, as well as a matrix representation. Several properties of the sequence of the maximum real roots will also be presented to explain the analytic behavior of Gn.

Comments

© 2025 The Author(s), under exclusive license to Springer Nature Switzerland AG

https://rdcu.be/eMBfI

Recommended Citation

Hallas, Kristen, Joan Mattle, Deanna Perez, and Aklilu Zeleke. "Some Remarks on Fibonacci-type Recursive Polynomials." In Southeastern International Conference on Combinatorics, Graph Theory, and Computing, pp. 15-29. Cham: Springer Nature Switzerland, 2023. https://doi.org/10.1007/978-3-031-83864-4_2

Publication Title

Combinatorics, Graph Theory and Computing

DOI

10.1007/978-3-031-83864-4_2