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 |
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Pages (from-to) | 76-138 |
Number of pages | 63 |
Journal | Advances in Applied Mathematics |
Volume | 96 |
DOIs | |
State | Published - May 2018 |
Bibliographical note
Publisher Copyright:© 2018 Elsevier Inc.
Keywords
- Maximal green sequence
- Quiver mutation
- Scattering diagram
- Triangulated surface
ASJC Scopus subject areas
- Applied Mathematics