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.
| Original language | English |
|---|---|
| Pages (from-to) | 76-138 |
| Number of pages | 63 |
| Journal | Advances in Applied Mathematics |
| Volume | 96 |
| DOIs | |
| State | Published - May 2018 |
Bibliographical note
Funding Information:Alexander Garver thanks Greg Muller and Rebecca Patrias for useful conversations. At various stages of this project, Alexander Garver received support from an RTG grant DMS-1148634 , NSERC grant RGPIN/05999-2014 , and the Canada Research Chairs program. Khrystyna Serhiyenko was supported by the NSF Postdoctoral Fellowship MSPRF-1502881 .
Funding Information:
Alexander Garver thanks Greg Muller and Rebecca Patrias for useful conversations. At various stages of this project, Alexander Garver received support from an RTG grant DMS-1148634, NSERC grant RGPIN/05999-2014, and the Canada Research Chairs program. Khrystyna Serhiyenko was supported by the NSF Postdoctoral Fellowship MSPRF-1502881.
Publisher Copyright:
© 2018 Elsevier Inc.
Keywords
- Maximal green sequence
- Quiver mutation
- Scattering diagram
- Triangulated surface
ASJC Scopus subject areas
- Applied Mathematics