Constructs all distributive lattices between weak and Bruhat orders in type A indexed by binary trees via root poset rectangles, proves uniqueness, and generalizes to minuscule middle orders as a subset of sorting orders in other Weyl groups.
Lattices of pretorsion classes
1 Pith paper cite this work. Polarity classification is still indexing.
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Middle orders: all distributive lattices between weak and Bruhat
Constructs all distributive lattices between weak and Bruhat orders in type A indexed by binary trees via root poset rectangles, proves uniqueness, and generalizes to minuscule middle orders as a subset of sorting orders in other Weyl groups.