Source characterization of the hypergraphic posets

2025/08/21 by Gélinas, Félix
#06B99 #52B11 #52B12 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.16006

Abstract

For a hypergraph ℍ on [n], the hypergraphic poset P_ℍ is the transitive closure of the oriented 1-skeleton of the hypergraphic polytope Δ_ℍ. In a recent paper, N. Bergeron and V. Pilaud provided a characterization of P_ℍ based on the sources of acyclic orientations for interval hypergraphs. The goal of this work is to extend this source characterization of P_ℍ for arbitrary hypergraphs on [n].

Citations

• Shuffles of deformed permutahedra, multiplihedra, constrainahedra, and biassociahedra
• Acyclic reorientation lattices and their lattice quotients
• Fertilitopes
• Lattices from graph associahedra and subalgebras of the Malvenuto-Reutenauer algebra
• Hopf monoids and generalized permutahedra
• On a special class of general permutahedra
• Lifted generalized permutahedra and composition polynomials
• The flag polynomial of the Minkowski sum of simplices
• The bitwisted Cartesian model for the free loop fibration
• Convex Hull Realizations of the Multiplihedra
• Faces of Generalized Permutohedra
• On Minkowski Sums of Simplices
• Permutohedra, associahedra, and beyond
• Matroid polytopes, nested sets and Bergman fans
• Realization of the Stasheff polytope
• A polytope related to empirical distributions, plane trees, parking functions, and the associahedron

Related

• Interval hypergraphic lattices
• Syntactic aspects of hypergraph polytopes
• Hypergraphic zonotopes and acyclohedra
• Ornamentation lattices and intreeval hypergraphic lattices
• Hypergraph Polytopes