A two dimensional lattice equation as an extension of the Heideman-Hogan recurrence

TL;DR

This paper introduces a two-dimensional lattice extension of the Heideman-Hogan recurrence, demonstrating its linearizability, Laurent property, and coprimeness, and explores its reductions and related higher-order equations.

Contribution

It presents a novel two-dimensional extension of the Heideman-Hogan recurrence, expanding the class of linearizable lattice equations with proven algebraic properties.

Findings

The lattice equation is linearizable in both directions.

It exhibits Laurent and coprimeness properties.

Reductions recover the original Heideman-Hogan recurrence.

Abstract

We consider a two dimensional extension of the so-called linearizable mappings. In particular, we start from the Heideman-Hogan recurrence, which is known as one of the linearizable Somos-like recurrences, and introduce one of its two dimensional extensions. The two dimensional lattice equation we present is linearizable in both directions, and has the Laurent and the coprimeness properties. Moreover, its reduction produces a generalized family of the Heideman-Hogan recurrence. Higher order examples of two dimensional linearizable lattice equations related to the Dana-Scott recurrence are also discussed.