Minimal length maximal green sequences

Alexander Garver, Thomas McConville, Khrystyna Serhiyenko

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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 languageEnglish
Pages (from-to)76-138
Number of pages63
JournalAdvances in Applied Mathematics
Volume96
DOIs
StatePublished - 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

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