Symmetric Solutions to Symmetric Partial Difference Equations

TL;DR

This paper investigates symmetric linear difference equations on integer lattices and demonstrates the existence of solutions that preserve the same symmetry group, advancing understanding of symmetric solutions in discrete systems.

Contribution

It proves the existence of symmetric solutions for systems of linear difference equations invariant under finite symmetry groups.

Findings

Existence of symmetric solutions proven

Solutions inherit the symmetry of the system

Applicable to systems on integer lattices

Abstract

This paper studies systems of linear difference equations on the lattice $\Z^n$ that are invariant under a finite group of symmetries, and shows that there exist solutions to such systems that are also invariant under this group of symmetries.