A Refined Denominator Bounding Algorithm for Multivariate Linear Difference Equations

TL;DR

This paper advances the understanding of denominator factors in rational solutions of multivariate linear difference equations by refining an algorithm to identify both periodic and aperiodic factors, improving prediction accuracy.

Contribution

It introduces a refined algorithm that effectively detects most periodic denominator factors in multivariate linear difference equations, extending previous methods focused on aperiodic factors.

Findings

The refined algorithm improves detection of periodic denominator factors.

The method enhances the prediction of rational solutions' denominators.

It extends previous algorithms to cover more cases of denominator factors.

Abstract

We continue to investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation. In an earlier article we had introduced the distinction between periodic and aperiodic factors in the denominator, and we gave an algorithm for predicting the aperiodic ones. Now we extend this technique towards the periodic case and present a refined algorithm which also finds most of the periodic factors.