def test_generate():
assert set(Permutation.fpf_involutions(2)) == {Permutation(2, 1)}
assert set(Permutation.fpf_involutions(3)) == set()
assert set(Permutation.fpf_involutions(4)) == {
Permutation(2, 1, 4, 3),
Permutation(3, 4, 1, 2),
Permutation(4, 3, 2, 1),
}
def test_involutions():
assert set(Permutation.involutions(1)) == {Permutation()}
assert set(Permutation.involutions(1, True)) == {Permutation(), Permutation(-1)}
assert set(Permutation.involutions(2)) == {Permutation(), Permutation(2, 1)}
assert set(Permutation.involutions(2, True)) == {
Permutation(),
Permutation(-1),
Permutation(2, 1),
Permutation(-2, -1),
Permutation(-1, -2),
Permutation(1, -2)
}
n = 6
assert set(Permutation.involutions(n)) == {
w for w in Permutation.all(n) if w.inverse() == w
}
assert set(Permutation.involutions(n, True)) == {
w for w in Permutation.all(n, True) if w.inverse() == w
}
assert len(set(Permutation.involutions(n))) == len(list(Permutation.involutions(n)))
assert set(Permutation.fpf_involutions(4)) == {
Permutation(2, 1, 4, 3),
Permutation(3, 4, 1, 2),
Permutation(4, 3, 2, 1),
}
def test_get_molecules_n(n=8):
ans = {}
fpf = set(Permutation.fpf_involutions(n))
bns = get_molecules_n(n)
for mu in bns:
molecule = molecule_n(mu)
fpf -= molecule
ans[mu] = molecule
assert len(fpf) == 0
assert all(ans[mu] == bns[mu] for mu in bns)
def test_bidirected_edges_m(n=8):
for w in Permutation.fpf_involutions(n):
p, _ = rsk(w)
for y, i in set(bidirected_edges_m(w)):
print(w, '<--', i, '-->', y)
q, _ = rsk(y)
print(p)
print(q)
print()
assert q == dual_equivalence(p, i)
def test_fpf_atoms():
y = Permutation(4, 3, 2, 1)
s = Permutation.s_i(1)
t = Permutation.s_i(2)
u = Permutation.s_i(3)
assert set(y.get_fpf_atoms()) == {t * s, t * u}
n = 6
for w in Permutation.fpf_involutions(n):
atoms = set()
for word in w.get_fpf_involution_words():
atoms.add(Permutation.from_word(word))
assert atoms == set(w.get_fpf_atoms())
def test_get_molecules_m(n=8):
ans = {}
inv = set(Permutation.fpf_involutions(n))
while inv:
w = inv.pop()
mu = rsk(w)[0].shape()
molecule = molecule_m(mu)
inv -= molecule
assert mu not in ans
ans[mu] = molecule
bns = get_molecules_m(n)
assert all(ans[mu] == bns[mu] for mu in bns)
assert all(representative_m(mu) in bns[mu] for mu in bns)
def get_molecules_m(n, verbose=False):
ans = {}
nn = double_fac(n - 1)
for i, w in enumerate(Permutation.fpf_involutions(n)):
mu = rsk(w)[0].shape()
if mu not in ans:
ans[mu] = set()
ans[mu].add(w)
if verbose:
a = nn - i
if a % 100 == 0:
print(a)
return ans
def test_six():
_test(Permutation.fpf_involutions(6), 6)
def test_four():
_test(Permutation.fpf_involutions(4), 8)
def test_three():
_test(Permutation.fpf_involutions(3), 10)
def test_two():
_test(Permutation.fpf_involutions(2), 8)
def test_one():
_test(Permutation.fpf_involutions(1), 12)