Derivations and identities for Fibonacci and Lucas polynomials
Rings and Algebras
2014-07-28 v2 Combinatorics
Number Theory
Abstract
We introduce the notion of Fibonacci and Lucas derivations of the polynomial algebras and prove that any element of kernel of the derivations defines a polynomial identity for the Fibonacci and Lucas polynomials. Also, we prove that any polynomial identity for Appel polynomial yields a polynomial identity for the Fibonacci and Lucas polynomials and describe the corresponding intertwining maps.
Keywords
Cite
@article{arxiv.1207.5891,
title = {Derivations and identities for Fibonacci and Lucas polynomials},
author = {Leonid Bedratyuk},
journal= {arXiv preprint arXiv:1207.5891},
year = {2014}
}
Comments
16 pages