Green-to-red sequences for positroids

Nicolas Ford, Khrystyna Serhiyenko

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


L-diagrams are combinatorial objects that parametrize cells of the totally nonnegative Grassmannian, called positroid cells, and each L-diagram gives rise to a cluster algebra which is believed to be isomorphic to the coordinate ring of the corresponding positroid variety. We study quivers arising from these diagrams and show that they can be constructed from the well-behaved quivers associated to Grassmannians by deleting and merging certain vertices. Then, we prove that quivers coming from arbitrary L-diagrams, and more generally reduced plabic graphs, admit a particular sequence of mutations called a green-to-red sequence.

Original languageEnglish
Pages (from-to)164-182
Number of pages19
JournalJournal of Combinatorial Theory. Series A
StatePublished - Oct 2018

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Inc.


  • Green-to-red sequence
  • Le-diagram
  • Plabic graph
  • Positroid
  • Quiver mutation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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