Abstract
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.
Originalsprache | englisch |
---|---|
Seiten (von - bis) | 479-504 |
Seitenumfang | 26 |
Fachzeitschrift | Combinatorica |
Jahrgang | 43 |
Ausgabenummer | 3 |
DOIs | |
Publikationsstatus | Veröffentlicht - Juni 2023 |
ASJC Scopus subject areas
- Diskrete Mathematik und Kombinatorik
- Computational Mathematics