cellOrder(MomentGraph,Poset) -- define a cell order on a moment graph

Synopsis

• Function: cellOrder

• Usage:

  cellOrder(G,P)

• Inputs:
  • G, a moment graph,
  • P, an instance of the type Poset, whose ground set is the vertices of G

Description

i2 : PP3 = projectiveSpace 3

o2 = a GKM variety with an action of a 4-dimensional torus

o2 : GKMVariety

i3 : cellOrder PP3
stdio:3:1:(3): error:  no cell order defined on this moment graph

i4 : V = (momentGraph PP3).vertices

o4 = {set {0}, set {1}, set {2}, set {3}}

o4 : List

i5 : P = poset(V, {{V_0,V_1},{V_1,V_2},{V_2,V_3}})

o5 = P

o5 : Poset

i6 : cellOrder(momentGraph PP3, P)

i7 : cellOrder PP3

o7 = P

o7 : Poset

See also

• cellOrder -- the poset of a stratification of a GKM variety
• bruhatOrder -- computes the Bruhat order on a generalized flag variety