Partial Denominator Bounds for Partial Linear Difference Equations

TL;DR

This paper extends denominator bounding techniques from univariate to multivariate partial linear difference equations, enabling the identification of all aperiodic denominator factors in rational solutions.

Contribution

It introduces a generalized method for finding aperiodic denominator factors in PLDEs, broadening the scope of existing univariate techniques.

Findings

Successfully generalized denominator bounds to multivariate equations

Identified all aperiodic factors in denominators of solutions

Enhanced understanding of rational solutions for PLDEs

Abstract

We investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation (PLDE). Two kinds of polynomials are to be distinguished, we call them /periodic/ and /aperiodic/. The main result is a generalization of a well-known denominator bounding technique for univariate equations to PLDEs. This generalization is able to find all the aperiodic factors of the denominators for a given PLDE.