Lengths of maximal green sequences for tame path algebras

Ryoichi Kase, Ken Nakashima

Research output: Contribution to journalArticlepeer-review


In this paper, we study the maximal length of maximal green sequences for quivers of type D~ and E~ by using the theory of tilting mutation. We show that the maximal length does not depend on the choice of the orientation and determine it explicitly. Moreover, we give a program which counts all maximal green sequences by length for a given Dynkin/extended Dynkin quiver.

Original languageEnglish
Article number59
JournalResearch in Mathematical Sciences
Issue number4
Publication statusPublished - Dec 2021
Externally publishedYes


  • (τ-)tilting theory
  • Maximal green sequence
  • Quiver representation
  • Support (τ-)tilting poset
  • Tame path algebra

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Mathematics (miscellaneous)
  • Computational Mathematics
  • Applied Mathematics


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