For rooted and unstarred increasing trees, the ornamentation lattice is a lattice quotient of the acyclic reorientation lattice and is realized by the path hypergraphic polytope, answering an open question of Defant and Sack.
Interval hypergraphic lattices
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Ornamentation lattices and intreeval hypergraphic lattices
For rooted and unstarred increasing trees, the ornamentation lattice is a lattice quotient of the acyclic reorientation lattice and is realized by the path hypergraphic polytope, answering an open question of Defant and Sack.