def test_skew_semistandard_setvalued():
n = 2
mu = (2, )
nu = (1, )
tabs = Tableau.semistandard_setvalued(n, mu, nu)
print(sorted(tabs))
assert tabs == {
Tableau({(1, 2): 1}),
Tableau({(1, 2): 2}),
Tableau({(1, 2): (1, 2)})
}
n = 2
mu = (1, 1)
nu = (1, )
tabs = Tableau.semistandard_setvalued(n, mu, nu)
print(sorted(tabs))
assert tabs == {
Tableau({(2, 1): 1}),
Tableau({(2, 1): 2}),
Tableau({(2, 1): (1, 2)})
}
def test_tableaux():
# generate tableaux and reverse plane partitions
from tableaux import Tableau
mu = (4, 2, 1)
a = Tableau.semistandard(3, mu)
b = Tableau.semistandard_setvalued(3, mu)
c = Tableau.semistandard_shifted(3, mu, diagonal_primes=True)
d = Tableau.semistandard_shifted_setvalued(4, mu, diagonal_primes=False)
e = Tableau.semistandard_rpp(3, mu)
f = Tableau.semistandard_shifted_rpp(3, mu, diagonal_nonprimes=False)
# serialize to change a Tableau into a dictionary
s = [t.serialize() for t in c]
def test_semistandard_setvalued():
mu = ()
assert Tableau.semistandard_setvalued(0, mu) == {Tableau()}
assert Tableau.semistandard_setvalued(1, mu) == {Tableau()}
assert Tableau.semistandard_setvalued(2, mu) == {Tableau()}
mu = (1, )
assert Tableau.semistandard_setvalued(1, mu) == {Tableau({(1, 1): 1})}
assert Tableau.semistandard_setvalued(2, mu) == {
Tableau({(1, 1): 1}),
Tableau({(1, 1): 2}),
Tableau({(1, 1): (1, 2)})
}
mu = (1, 1)
assert Tableau.semistandard_setvalued(
2, mu) == {Tableau({
(1, 1): 1,
(2, 1): 2
})}
mu = (2, )
assert Tableau.semistandard_setvalued(2, mu) == {
Tableau({
(1, 1): 1,
(1, 2): 1
}),
Tableau({
(1, 1): 1,
(1, 2): 2
}),
Tableau({
(1, 1): 2,
(1, 2): 2
}),
Tableau({
(1, 1): 1,
(1, 2): (1, 2)
}),
Tableau({
(1, 1): (1, 2),
(1, 2): 2
}),
}
def _slow_stable_grothendieck(cls, num_variables, mu, nu=()):
return BETA**(sum(nu) - sum(mu)) * cls._slow_vectorize(
num_variables, Tableau.semistandard_setvalued(
num_variables, mu, nu), BETA)