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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