Minimal Length Maximal Green Sequences and Triangulations of Polygons

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.

22 pages, 1 figure

References in corpus (3)

• Maximal Green Sequences for Cluster Algebras Associated to the n-Torus
• Remarks on lengths of maximal green sequences for quivers of type ${\tilde{A}}_{n,1}$
• Maximal Green Sequences for Cluster Algebras Associated to the Orientable Surfaces of Genus n with Arbitrary Punctures