Minimal length maximal green sequences
Combinatorics
2018-09-06 v1 Representation Theory
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 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.
Keywords
Cite
@article{arxiv.1702.07313,
title = {Minimal length maximal green sequences},
author = {Alexander Garver and Thomas McConville and Khrystyna Serhiyenko},
journal= {arXiv preprint arXiv:1702.07313},
year = {2018}
}
Comments
43 pages, many figures, comments welcome