2024/11/14 by Nantel Bergeron, Vincent Pilaud, Bergeron, Nantel +1 · 1 citation
Computer Science · #06B99 #06D99 #52B11 #52B12 #Combinatorics (math.CO) #FOS: Mathematics #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2411.09832
openalex publication_date 2024/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a hypergraph ℍ on [n], the hypergraphic poset P_ℍ is the transitive closure of the oriented skeleton of the hypergraphic polytope \triangle_ℍ (the Minkowski sum of the standard simplices \triangleH for all H ∈ ℍ). Hypergraphic posets include the weak order for the permutahedron (when ℍ is the complete graph on [n]) and the Tamari lattice for the associahedron (when ℍ is the set of all intervals of [n]), which motivates the study of lattice properties of hypergraphic posets. In this paper, we focus on interval hypergraphs, where all hyperedges are intervals of [n]. We characterize the interval hypergraphs \mathbbI for which P_\mathbbI is a lattice, a distributive lattice, a semidistributive lattice, and a lattice quotient of the weak order.