def leq(self, R, S):
if R not in self.schubert_list or S not in self.schubert_list:
raise ValueError('input not an index set in this Grassmannian!')
for i in range(self.m):
if R[i] > S[i]:
return False
if self.type == 'D':
if self.involve:
return pf.perm_leq(self.type,self.index2perm(R),self.index2perm(S))
else:
return pf.perm_geq(self.type,self.index2perm(R),self.index2perm(S))
return True
def bad_reflections(g,T): perm = g.index2perm(T) refs = g.simple_reflections() for s in refs: a = [] for P in g.schubert_list: if pf.perm_leq(g.type,pf.perm_mult(perm,s),g.index2perm(P)): a.append(P) m = [] for P in a: minimal = True for Q in a: if g.leq(Q,P) and Q != P: minimal = False if minimal: m.append(g.index2perm(P)) print 'minimal signed permutations violating reflection ' + str(s) + ':' print m
def leq(self, u, v):
if u not in self.perm_list or v not in self.perm_list:
raise ValueError('input not a valid permutation for this flag variety!')
return pf.perm_leq(self.type,u,v)
