## Abstract

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 language | English |
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Article number | #42 |

Journal | Seminaire Lotharingien de Combinatoire |

Issue number | 85 |

State | Published - 2021 |

### Bibliographical note

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

## Keywords

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

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics