On some classes of discrete polynomials and ordinary difference equations

TL;DR

This paper introduces new classes of discrete polynomials and constructs integrable discrete equations with Lax representations, providing a method to explicitly build lattice integrable hierarchies and illustrating the approach with examples.

Contribution

It presents novel classes of discrete polynomials and a systematic approach to construct lattice integrable hierarchies with explicit forms.

Findings

New classes of discrete polynomials introduced.

Discrete equations with Lax representations constructed.

Explicit lattice integrable hierarchies demonstrated.

Abstract

We introduce two classes of discrete polynomials and construct discrete equations admitting a Lax representation in terms of these polynomials. Also we give an approach which allows to construct lattice integrable hierarchies in its explicit form and show some examples.