A Unifying Framework for the ν -Tamari Lattice and Principal Order Ideals in Young’s Lattice

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

Research output: Contribution to journalArticlepeer-review


We present a unifying framework in which both the ν -Tamari lattice, introduced by Préville-Ratelle and Viennot, and principal order ideals in Young’s lattice indexed by lattice paths ν , are realized as the dual graphs of two combinatorially striking triangulations of a family of flow polytopes which we call the ν -caracol flow polytopes. The first triangulation gives a new geometric realization of the ν -Tamari complex introduced by Ceballos et al. We use the second triangulation to show that the h -vector of the ν -caracol flow polytope is given by the ν -Narayana numbers, extending a result of Mészáros when ν is a staircase lattice path. Our work generalizes and unifies results on the dual structure of two subdivisions of a polytope studied by Pitman and Stanley.

Original languageEnglish
Pages (from-to)479-504
Number of pages26
Issue number3
StatePublished - Jun 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature.


  • Flow polytope
  • Triangulation
  • Young’s lattice
  • ν-Dyck path
  • ν-Tamari lattice

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics


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