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.
Higher Bruhat orders of types B and C
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abstract
We propose versions of higher Bruhat orders for types $B$ and $C$. This is based on a theory of higher Bruhat orders of type~A and their geometric interpretations (due to Manin--Shekhtman, Voevodskii--Kapranov, and Ziegler), and on our study of the so-called symmetric cubillages of cyclic zonotopes.
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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.