# Minimal length maximal green sequences

## TL;DR

This paper provides a formula for the length of minimal length maximal green sequences in quivers derived from surface triangulations, advancing understanding in representation theory and related fields.

## Contribution

It introduces a novel combinatorial approach combining surface triangulations and scattering diagrams to determine minimal sequence lengths.

## Key findings

- Derived a formula for minimal length maximal green sequences
- Applied combinatorics of surface triangulations and scattering diagrams
- Focused on quivers from annulus and punctured disk triangulations

## Abstract

Maximal green sequences are important objects in representation theory, cluster algebras, and string theory. It is an open problem to determine what lengths are achieved by the maximal green sequences of a quiver. We combine the combinatorics of surface triangulations and the basics of scattering diagrams to address this problem. Our main result is a formula for the length of minimal length maximal green sequences of quivers defined by triangulations of an annulus or a punctured disk.