2021/01/25 by Matias von Bell, Rafael S. González D’León, von Bell, Matias +5 · 1 citation
Mathematics · #52B05 #52B11 #52B20 #52B22 (Primary) 05C21 (Secondary) #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2101.10425
openalex publication_date 2021/01/25 · openalex created_date 2023/06/14 · openalex updated_date 2026/07/28
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, Padrol and Sarmiento. 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.