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Séminaire Lotharingien de Combinatoire, 78B.16 (2017), 12 pp.

# Alexander Garver, Thomas McConville
amd Khrystyna Serhiyenko

# Minimal Length Maximal Green Sequences

**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 maximal green sequences of a
quiver. We use the combinatorics of surface triangulations 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.

Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.

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