def representative_n(mu):
shape = {(i, j): (i, min(j, mu[i - 1] + 1 - j)) if j !=
(mu[i - 1] + 1 - j) else (2 * ((i + 1) // 2), j)
for (i, j) in Partition.shape(mu)}
word = [
shape[key] for key in sorted(shape, key=lambda ij: (ij[1], -ij[0]))
]
pairs = defaultdict(list)
for i, key in enumerate(word):
pairs[key].append(i + 1)
w = Permutation()
for pair in pairs.values():
i, j = tuple(pair)
w *= Permutation.transposition(i, j)
return w
def anti_representative_m(mu):
t = Tableau(
{box: i + 1
for i, box in enumerate(sorted(Partition.shape(mu)))})
oneline, _ = InsertionAlgorithm.inverse_hecke(t, t)
return Permutation(*oneline)