### arXiv:1702.07313 [math.CO]AbstractReferencesReviewsResources

#### Minimal length maximal green sequences

Alexander Garver, Thomas McConville, Khrystyna Serhiyenko

Published 2017-02-23Version 1

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.

**Comments:**43 pages, many figures, comments welcome

arXiv:1603.06827 [math.CO] (Published 2016-03-22)

A new expander and improved bounds for $A(A+A)$

arXiv:1504.02650 [math.CO] (Published 2015-04-10)

Transversals in $4$-Uniform Hypergraphs

arXiv:1110.1240 [math.CO] (Published 2011-10-06)

On Graphs with the Smallest Eigenvalue at Least $-1-\sqrt{2}$, part II