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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