On a generalized $k$-FL sequence and its applications

TL;DR

This paper introduces a generalized $k$-FL sequence, explores related real number pairs, and applies these concepts to integral solutions of equations and matrix determinantal varieties.

Contribution

It presents a novel generalized $k$-FL sequence, analyzes associated real pairs, and studies matrix properties and applications related to these sequences.

Findings

Derived integral solutions for specific equations.

Analyzed determinantal varieties of associated matrices.

Established properties of skew circulant and circulant matrices.

Abstract

We introduce a generalized $k$-FL sequence and special kind of pairs of real numbers that are related to it, and give an application on the integral solutions of a certain equation using those pairs. Also, we associate skew circulant and circulant matrices to each generalized $k$-FL sequence, and study the determinantal variety of those matrices as an application.