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.
|State||Published - 2006|
|Event||29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017 - London, United Kingdom|
Duration: Jul 9 2017 → Jul 13 2017
|Conference||29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017|
|Period||7/9/17 → 7/13/17|
Bibliographical noteFunding Information:
A. Garver received support from an RTG grant DMS-1148634, NSERC, and the Canada Research Chairs program. K. Serhiyenko was supported by the NSF Postdoctoral Fellowship MSPRF-1502881. The authors are grateful to the referees for their careful comments.
© 29th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.
- Maximal green sequence
- Quiver mutation
- Triangulated surface
ASJC Scopus subject areas
- Algebra and Number Theory