Matroids arisen from seeds

TL;DR

This paper introduces and explores cluster matroids, a new class of matroids derived from cluster algebras, analyzing their properties and relationships with uniform matroids.

Contribution

It defines cluster matroids, investigates their properties, and establishes connections with uniform matroids and their minors.

Findings

Cluster matroids form a new subclass of matroids.

Relationships between cluster and uniform matroids are characterized.

Properties and minors of cluster matroids are analyzed.

Abstract

This study aims to shed light on new (sub)classes of matroids originating from cluster algebras and investigate their properties. We focus on what we call cluster matroids and build some results on them. Then, we point out a relationship between these kinds of matroids and uniform matroids and study their minors.