# New identities for some symmetric polynomials, and a higher order analogue of the Fibonacci and Lucas numbers

## TL;DR

This paper introduces new identities for symmetric polynomials and applies them to derive formulas for higher order analogues of Fibonacci and Lucas numbers, expanding understanding of these classical sequences.

## Contribution

It presents novel identities for symmetric polynomials and uses them to develop higher order Fibonacci and Lucas number formulas, a new approach in this area.

## Key findings

- New identities for symmetric polynomials
- Formulas for higher order Fibonacci numbers
- Formulas for higher order Lucas numbers

## Abstract

We give new identities for some symmetric polynomials. As applications of these identities, we obtain some formulas for a higher order analogue of Fibonacci and Lucas numbers.