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Interval hypergraphic lattices
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For a hypergraph ℍ on [ ] , the hypergraphic poset ℍ
is the transitive closure of the oriented skeleton of the hypergraphic polytope △ℍ
(the Minkowski sum of the standard simplices △ for all ∈ℍ
). Hypergraphic posets include the weak order for the permutahedron (when ℍ
is the complete graph on [ ] ) and the Tamari lattice for the associahedron (when ℍ
is the set of all intervals of [ ] ), which motivates the study of lattice properties of hypergraphic posets. In this paper, we focus on interval hypergraphs, where all hyperedges are intervals of [ ] . We characterize the interval hypergraphs
for which is a lattice, a distributive lattice, a semidistributive lattice, and a lattice quotient of the weak order.
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BERGERON, Nantel and PILAUD, Vincent. Interval hypergraphic lattices. European Journal of Combinatorics. 2026. Vol. 132, num. B. ISSN 0195-6698. [consulted: 26 of September of 2026]. Available at: https://hdl.handle.net/2445/231626