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GKMVarieties :: bruhatOrder

bruhatOrder -- computes the Bruhat order on a generalized flag variety



Given a GKMVariety $X$ created by either generalizedFlagVariety or generalizedSchubertVariety, computes and returns the Bruhat order corresponding to the Bruhat decomposition. The resulting poset is cached in $X$, and can be accessed by either cellOrder or bruhatOrder.

i1 : Fl3 = generalizedFlagVariety("A",2,{1,2})

o1 = a GKM variety with an action of a 3-dimensional torus

o1 : GKMVariety
i2 : cellOrder Fl3
stdio:2:1:(3): error:  no cell order defined on this moment graph
i2 : P = bruhatOrder Fl3

o2 = P

o2 : Poset
i3 : #(coveringRelations P) == 8

o3 = true
i4 : cellOrder Fl3

o4 = P

o4 : Poset

See also

Ways to use bruhatOrder :

For the programmer

The object bruhatOrder is a method function.