Some results about Linear Recurrence Relation Homomorphisms

TL;DR

This paper introduces the concept of recurrence relation homomorphisms, explores their properties, and investigates the periodicity of linear recurrence relations, providing foundational results and illustrative examples.

Contribution

It defines recurrence relation homomorphisms and analyzes the period of linear recurrence relations, offering new theoretical insights and initial results.

Findings

Definition of recurrence relation homomorphism

Period analysis of linear recurrence relations

Preliminary results on recurrence relation periodicity

Abstract

In this paper we propose a definition of a recurrence relation homomorphism and illustrate our definition with a few examples. We then define the period of a k-th order of linear recurrence relation and deduce certain preliminary results associated with them.