Linear Laurent phenomenon algebras

TL;DR

This paper provides an explicit description of Laurent phenomenon algebras with linear initial seeds derived from graphs, linking graph associahedra to the dual cluster complex within this algebraic framework.

Contribution

It introduces a detailed description of Laurent phenomenon algebras from graphs and connects graph associahedra to the dual cluster complex.

Findings

Graph associahedra are dual cluster complexes of certain Laurent phenomenon algebras.

Explicit descriptions of these algebras with linear initial seeds are provided.

The work generalizes cluster algebra concepts to a broader algebraic setting.

Abstract

In [LP] we introduced Laurent phenomenon algebras, a generalization of cluster algebras. Here we give an explicit description of Laurent phenomenon algebras with a linear initial seed arising from a graph. In particular, any graph associahedron is shown to be the dual cluster complex for some Laurent phenomenon algebra.