def get_inv_grassmannian(cls, *mu):
assert Partition.is_strict_partition(mu)
ans = Permutation()
for i in range(len(mu)):
ans *= Permutation.transposition(1 + mu[0] - mu[i], i + 1 + mu[0])
w0 = Permutation.longest_element(len(mu) + (mu[0] if mu else 0))
ans = w0 * ans * w0
return ans
def get_fpf_grassmannian(cls, *mu):
assert Partition.is_strict_partition(mu)
ans = Permutation()
o = 1 if (mu and (len(mu) + 1 + mu[0]) % 2 != 0) else 0
for i in range(len(mu)):
ans *= Permutation.transposition(o + 1 + mu[0] - mu[i], o + i + 2 + mu[0])
while not ans.is_fpf_involution():
f = [i for i in range(1, ans.rank + 2) if ans(i) == i]
ans *= Permutation.transposition(f[0], f[1])
w0 = Permutation.longest_element(o + 1 + len(mu) + (mu[0] if mu else 0))
ans = w0 * ans * w0
return ans