Edge-labelled polygonal lattices carry preorders on square-equivalence classes of maximal chains that descend to contractions under lattice quotients, yielding new structural results for Cambrian lattices and the Kapranov-Voevodsky map.
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Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences
Edge-labelled polygonal lattices carry preorders on square-equivalence classes of maximal chains that descend to contractions under lattice quotients, yielding new structural results for Cambrian lattices and the Kapranov-Voevodsky map.