def test_star(n=8):
for nu in Partition.generate(n, even_parts=True):
mu = Partition.transpose(nu)
lu = Partition.transpose(tuple(2 * mu[i]
for i in range(0, len(mu), 2)))
assert mu == Partition.transpose(
tuple(2 * lu[i] for i in range(0, len(lu), 2)))
def _vertical_strips(cls, mu, lam):
ans = []
strips = cls._horizontal_strips(Partition.transpose(mu),
Partition.transpose(lam))
for nu, diff, corners in strips:
nu = Partition.transpose(nu)
diff = {(j, i) for (i, j) in diff}
corners = [(j, i) for (i, j) in corners]
ans.append((nu, diff, corners))
return ans
def test_anti_representatives(n=8):
for nu in Partition.generate(n, even_parts=True):
mu = Partition.transpose(nu)
lu = Partition.transpose(tuple(2 * mu[i]
for i in range(0, len(mu), 2)))
print(mu)
print(lu)
print()
assert representative_m(lu) == anti_representative_n(mu)
def test_molecular_correspondence(n=8):
for mu in Partition.generate(n, even_parts=True):
mu = Partition.transpose(mu)
mapping = construct_molecular_correspondence(mu)
for v in mapping:
w = mapping[v]
assert irsk(v).transpose() == dual_irsk(w)
def get_molecules_n(n, verbose=False):
ans = {}
for mu in Partition.generate(n, even_parts=True):
mu = Partition.transpose(mu)
molecule = molecule_n(mu)
ans[mu] = molecule
return ans
def representative_m(mu):
a = 0
w = Permutation()
for b in Partition.transpose(mu):
for i in range(b // 2):
w *= Permutation.transposition(a + i + 1, a + b - i)
a += b
return w
def test_symmetric(n=4):
a = {(i, j) for i in range(1, n + 1) for j in range(1, i + 1)}
for k in range(len(a)):
for _subset in itertools.combinations(a, k):
subset = set(_subset) | {(j, i) for (i, j) in _subset}
dictionary = {}
for (i, j) in subset:
x = random.randint(1, 10)
dictionary[(i, j)] = x
dictionary[(j, i)] = x
g = Partition.growth_diagram(dictionary, n, n)
# Partition.print_growth_diagram(g)
for i in range(n + 1):
mu = Partition.transpose(g[i][i])
sigma = sum([dictionary.get((j, j), 0) for j in range(i + 1)])
emp = sum([abs(v % 2) for v in mu])
assert emp == sigma
def print_molecular_correspondence(n=8):
def wstr(w):
return ' $\\barr{c}' + str(
w) + ' \\\\ ' + w.oneline_repr() + ' \\earr$ '
ans = []
for n in range(2, n + 1, 2):
for mu in Partition.generate(n, even_parts=True):
s = []
mu = Partition.transpose(mu)
mapping = construct_molecular_correspondence(mu)
i = 0
for v in mapping:
w = mapping[v]
# w = w * Permutation.longest_element(n)
t, _ = rsk(v)
p, q = rsk(w, n)
s += [
'\n&\n'.join(
[wstr(v),
t.tex(),
wstr(w),
dual_irsk(w).tex()])
]
i += 1
if i * t.max_row() >= 24:
s += [
'\n\\end{tabular} \\newpage \\begin{tabular}{ccccc}\nM & Tableau & N & & \\\\ \\hline '
]
i = 0
s = '\n \\\\ \\\\ \n'.join(s)
ans += [
'\\begin{tabular}{ccccc}\nM & Tableau & N & & \\\\ \\hline \\\\ \\\\ \n'
+ s + '\n\\end{tabular}'
]
ans = '\n\n\\newpage\n\n'.join(ans + [''])
with open(
'/Users/emarberg/Dropbox/projects/affine-transitions/notes/eric_notes/examples.tex',
'w') as f:
f.write(ans)
f.close()
def _rpp_vertical_strips(cls, mu, lam): # noqa
strips = cls._rpp_horizontal_strips(Partition.transpose(mu),
Partition.transpose(lam))
return [(Partition.transpose(nu), {(j, i)
for i, j in diff})
for nu, diff in strips]
def test_tilde_representatives(n=8):
for nu in Partition.generate(n):
w = tilde_representative_n(nu)
v = anti_representative_m(Partition.transpose(nu))
assert w == v