On framed triangulations of flow polytopes, the v-Tamari lattice and Young’s lattice

Matias von Bell, Rafael S.González D’León, Francisco A.Mayorga Cetina, Martha Yip

Research output: Contribution to journalArticlepeer-review


We study two combinatorially striking triangulations of a family of flow polytopes indexed by lattice paths v which we call the v-caracol flow polytopes. The first triangulation gives a geometric realization of the v-Tamari complex introduced by Ceballos, Padrol and Sarmiento, whose dual graph is the Hasse diagram of the v-Tamari lattice introduced by Préville-Ratelle and Viennot. The dual graph of the second triangulation is the Hasse diagram of the principal order ideal determined by v in Young’s lattice. We use the latter triangulation to show that the h*-vector of the v-caracol flow polytope is given by the v-Narayana numbers, extending the result of Mészáros when v is a staircase lattice path.

Original languageEnglish
Article number#42
JournalSeminaire Lotharingien de Combinatoire
Issue number85
StatePublished - 2021

Bibliographical note

Publisher Copyright:
© 2021, Seminaire Lotharingien de Combinatoire.All Rights Reserved.


  • Young’s lattice
  • flow polytope
  • triangulation
  • v-Dyck path
  • v-Tamari lattice

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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