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 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 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 print_mn_operators(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):
s = []
i = 0
for t in Tableau.standard(mu):
u = dual_irsk(irsk_inverse(t), n).transpose()
s += ['\n&\n'.join([t.tex(), u.tex()])]
i += 1
if i * t.max_row() >= 24:
s += [
'\n\\end{tabular} \\newpage \\begin{tabular}{ccccc} Tableau & Tableau \\\\ \\hline '
]
i = 0
s = '\n \\\\ \\\\ \n'.join(s)
ans += [
'\\begin{tabular}{ccccc} Tableau & Tableau \\\\ \\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 print_tableau_operation(n=6):
mapping = {}
for mu in Partition.generate(n):
for tab in Tableau.standard(mu):
w = irsk_inverse(tab)
ntab = dual_irsk(w, sum(mu)).transpose()
mapping[tab] = ntab
print(tab)
print('w =', w)
print(ntab)
#lines = str(tab).split('\n')
#nlines = str(ntab).split('\n')
#assert len(lines) == len(nlines)
#print('\n'.join([lines[i] + ' -> ' + nlines[i] for i in range(len(lines))]))
print()
print()
print()
print()
orders = {}
for tab in mapping:
o = 1
x = mapping[tab]
while x != tab:
o += 1
x = mapping[x]
orders[tab] = o
return orders, mapping
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_from_string(m=4):
for n in range(m):
for mu in Partition.generate(n, strict=True):
for t in Tableau.semistandard_shifted_marked(n, mu):
u = Tableau(str(t))
if u != t:
print(t)
print(u)
print(t.boxes, u.boxes)
print()
assert Tableau(str(t)) == t
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 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