def _KOG_count_helper(cls, p, rim): # noqa
if len(rim) == 0:
return 1 if p == 0 else 0
if p <= 0:
return 0
term = Partition.rim_terminal_part(rim)
if len(term) == 2 and p == 1:
return 0
elif len(term) == 2:
left = tuple(a for a in rim if a not in term)
x = cls._KOG_count_helper(p, left)
y = cls._KOG_count_helper(p - 1, left)
z = cls._KOG_count_helper(p - 2, left)
c = 2 if p > 2 else 1
return x + (1 + c) * y + c * z
else:
left = tuple(a for a in rim if a != term[-1])
x = cls._KOG_count_helper(p, left)
y = cls._KOG_count_helper(p - 1, left)
c = 2 if p > 1 else 1
if len(term) == 1:
return c * (x + y)
if len(term) == 3 and term[0][0] != term[-1][0] and term[0][
1] != term[-1][1]:
return x + y
if len(term) == 3:
return y
def print_rshape(nu, mu, lam):
lines = []
for i in range(1, len(nu) + 1):
line = (i - 1) * [' '] + Partition.get(mu, i) * ['.']
line += (Partition.get(lam, i) - Partition.get(mu, i)) * ['R']
line += (Partition.get(nu, i) - Partition.get(lam, i)) * ['*']
lines += [' '.join(line)]
print('\n'.join(reversed(lines)) + '\n')
print('term:', Partition.rim_terminal_part(right_rim(nu, mu, lam)))
print()
def split(nu, mu):
if (nu, mu) not in SPLIT_CACHE:
i, j = None, None
for lam in lshapes(nu, mu):
term = Partition.rim_terminal_part(left_rim(nu, mu, lam))
i = max(([] if i is None else [i]) + [a for (a, _) in term])
j = min(([] if j is None else [j]) + [b for (_, b) in term])
for lam in rshapes(nu, mu):
term = Partition.rim_terminal_part(right_rim(nu, mu, lam))
i = max(([] if i is None else [i]) + [a for (a, _) in term])
j = min(([] if j is None else [j]) + [b for (_, b) in term])
skew = Partition.skew(nu, mu, shifted=True)
# new_nu = Partition.trim(tuple(min(nu[t], j - t - 1) for t in range(i)) + nu[i:])
# new_mu = Partition.trim(tuple(min(mu[t], j - t - 1) for t in range(i)) + mu[i:])
while (i + 1, j) in skew:
i += 1
rest = {(a, b) for (a, b) in skew if (a <= i or b >= j)}
split_nu, split_mu = Partition.from_skew(rest, shifted=False)
diagonal = any(a == b for (a, b) in skew)
SPLIT_CACHE[(nu, mu)] = (split_nu, split_mu, diagonal)
return SPLIT_CACHE[(nu, mu)]
def _KLG_count_helper(cls, p, rim): # noqa
if len(rim) == 0:
return 1 if p == 0 else 0
if p <= 0:
return 0
term = Partition.rim_terminal_part(rim)
if len(term) == 2:
left = tuple(a for a in rim if a not in term)
x = cls._KLG_count_helper(p, left)
y = cls._KLG_count_helper(p - 1, left)
z = cls._KLG_count_helper(p - 2, left)
if p > 2:
return x + 3 * y + 2 * z
elif p == 2 and term[0][0] == term[0][1]:
return 1
elif p == 2:
return x + 3 * y + 2 * z
elif p == 1:
if term[0][0] == term[0][1] == term[1][0]:
return 0
elif term[0][0] == term[0][1] == term[1][1]:
return 1
else:
return x + y
else:
left = tuple(a for a in rim if a != term[-1])
x = cls._KLG_count_helper(p, left)
y = cls._KLG_count_helper(p - 1, left)
if len(term) == 1:
if p == 1 and term[0][0] == term[0][1]:
return 1
else:
return 2 * x + 2 * y
if len(term) == 3 and term[0][0] != term[-1][0] and term[0][
1] != term[-1][1]:
return x + y
if len(term) == 3:
return y