An infinite family of homogeneous discrete equations with the Laurent property

TL;DR

This paper introduces a new infinite family of homogeneous discrete equations with the Laurent property, expanding understanding of such equations, starting with the well-known Somos-5 recurrence.

Contribution

It presents a novel infinite family of equations with the Laurent property, generalizing the Somos-5 recurrence and exploring their properties.

Findings

The family includes the Somos-5 recurrence as a special case.

The equations in the family possess the Laurent property.

The paper investigates structural and algebraic properties of these equations.

Abstract

We present and investigate a new infinite family of homogeneous equations which possess the Laurent property. The first representative in this family is the well-known Somos-5 recurrence.