Minimal Length Maximal Green Sequences and Triangulations of Polygons

TL;DR

This paper investigates minimal length maximal green sequences for type A quivers, establishing their length as a sum of vertices and 3-cycles, and provides a method to construct such sequences.

Contribution

It characterizes the minimal length of maximal green sequences for type A quivers and introduces a procedure to generate them.

Findings

Minimal length sequences have length n + t.

A procedure to construct minimal length sequences.

The length depends on vertices and 3-cycles.

Abstract

We use combinatorics of quivers and the corresponding surfaces to study maximal green sequences of minimal length for quivers of type $\mathbb{A}$. We prove that such sequences have length $n+t$, where $n$ is the number of vertices and $t$ is the number of 3-cycles in the quiver. Moreover, we develop a procedure that yields these minimal length maximal green sequences.