def __classcall_private__(cls, x):
"""
Construct a multi skew tableau.
EXAMPLES::
sage: s = MultiSkewTableau([ [[None,1],[2,3]], [[1,2],[2]] ])
"""
if isinstance(x, MultiSkewTableau):
return x
return MultiSkewTableaux()([SkewTableau(i) for i in x])
def __init__(self, parent, t):
"""
Initialize ``self``.
EXAMPLES::
sage: R = RibbonShapedTableau([[2,3],[1,4,5]])
sage: TestSuite(R).run()
"""
if not isinstance(t, SkewTableau):
#scrubing None
t = [ [i for i in row if i is not None] for row in t]
st = []
space_count = 0
for row in reversed(t):
st.append( [None]*space_count + row )
space_count += len(row) - 1
st.reverse()
t = st
else:
t = list(t)
SkewTableau.__init__(self, parent, t)
def __init__(self, parent, t):
"""
Initialize ``self``.
EXAMPLES::
sage: R = RibbonShapedTableau([[2,3],[1,4,5]])
sage: TestSuite(R).run()
"""
if not isinstance(t, SkewTableau):
#scrubing None
t = [ [i for i in row if i is not None] for row in t]
st = []
space_count = 0
for row in reversed(t):
st.append( [None]*space_count + row )
space_count += len(row) - 1
st.reverse()
t = st
else:
t = list(t)
SkewTableau.__init__(self, parent, t)
def to_tableau(self):
r"""
Return the skew tableau associated to ``self``.
EXAMPLES::
sage: T = path_tableaux.DyckPath([0,1,2,3,2,3])
sage: T.to_tableau()
[[1, 2, 3, 5], [4]]
sage: U = path_tableaux.DyckPath([2,3,2,3])
sage: U.to_tableau()
[[None, None, 1, 3], [2]]
"""
w = self.to_word()
top = [i + 1 for i, a in enumerate(w) if a == 1]
bot = [i + 1 for i, a in enumerate(w) if a == 0]
if self.is_skew():
return SkewTableau([[None] * self[0] + top, bot])
else:
return StandardTableau([top, bot])
def insertion_tableau(skp, perm, evaluation, tableau, length):
"""
INPUT:
- ``skp`` -- skew partitions
- ``perm, evaluation`` -- non-negative integers
- ``tableau`` -- skew tableau
- ``length`` -- integer
TESTS::
sage: from sage.combinat.ribbon_tableau import insertion_tableau
sage: insertion_tableau([[1], []], [1], 1, [[], []], 1)
[[], [[1]]]
sage: insertion_tableau([[2, 1], []], [1, 1], 2, [[], [[1]]], 1)
[[], [[2], [1, 2]]]
sage: insertion_tableau([[2, 1], []], [0, 0], 3, [[], [[2], [1, 2]]], 1)
[[], [[2], [1, 2]]]
sage: insertion_tableau([[1, 1], []], [1], 2, [[], [[1]]], 1)
[[], [[2], [1]]]
sage: insertion_tableau([[2], []], [0, 1], 2, [[], [[1]]], 1)
[[], [[1, 2]]]
sage: insertion_tableau([[2, 1], []], [0, 1], 3, [[], [[2], [1]]], 1)
[[], [[2], [1, 3]]]
sage: insertion_tableau([[1, 1], []], [2], 1, [[], []], 2)
[[], [[1], [0]]]
sage: insertion_tableau([[2], []], [2, 0], 1, [[], []], 2)
[[], [[1, 0]]]
sage: insertion_tableau([[2, 2], []], [0, 2], 2, [[], [[1], [0]]], 2)
[[], [[1, 2], [0, 0]]]
sage: insertion_tableau([[2, 2], []], [2, 0], 2, [[], [[1, 0]]], 2)
[[], [[2, 0], [1, 0]]]
sage: insertion_tableau([[2, 2], [1]], [3, 0], 1, [[], []], 3)
[[1], [[1, 0], [0]]]
"""
psave = Partition(skp[1])
partc = skp[1] + [0] * (len(skp[0]) - len(skp[1]))
tableau = SkewTableau(expr=tableau).to_expr()[1]
for k in range(len(tableau)):
tableau[-(k + 1)] += [0] * (skp[0][k] - partc[k] -
len(tableau[-(k + 1)]))
## We construct a tableau from the southwest corner to the northeast one
tableau = [[0] * (skp[0][k] - partc[k])
for k in reversed(range(len(tableau), len(skp[0])))] + tableau
tableau = SkewTableaux().from_expr([skp[1], tableau]).conjugate()
tableau = tableau.to_expr()[1]
skp = SkewPartition(skp).conjugate().to_list()
skp[1].extend([0] * (len(skp[0]) - len(skp[1])))
if len(perm) > len(skp[0]):
return None
for k in range(len(perm)):
if perm[-(k + 1)] != 0:
tableau[len(tableau) - len(perm) +
k][skp[0][len(perm) - (k + 1)] -
skp[1][len(perm) - (k + 1)] - 1] = evaluation
return SkewTableau(expr=[psave.conjugate(), tableau]).conjugate().to_expr()
def insertion_tableau(skp, perm, evaluation, tableau, length):
"""
INPUT:
- ``skp`` -- skew partitions
- ``perm, evaluation`` -- non-negative integers
- ``tableau`` -- skew tableau
- ``length`` -- integer
TESTS::
sage: from sage.combinat.ribbon_tableau import insertion_tableau
sage: insertion_tableau([[1], []], [1], 1, [[], []], 1)
[[], [[1]]]
sage: insertion_tableau([[2, 1], []], [1, 1], 2, [[], [[1]]], 1)
[[], [[2], [1, 2]]]
sage: insertion_tableau([[2, 1], []], [0, 0], 3, [[], [[2], [1, 2]]], 1)
[[], [[2], [1, 2]]]
sage: insertion_tableau([[1, 1], []], [1], 2, [[], [[1]]], 1)
[[], [[2], [1]]]
sage: insertion_tableau([[2], []], [0, 1], 2, [[], [[1]]], 1)
[[], [[1, 2]]]
sage: insertion_tableau([[2, 1], []], [0, 1], 3, [[], [[2], [1]]], 1)
[[], [[2], [1, 3]]]
sage: insertion_tableau([[1, 1], []], [2], 1, [[], []], 2)
[[], [[1], [0]]]
sage: insertion_tableau([[2], []], [2, 0], 1, [[], []], 2)
[[], [[1, 0]]]
sage: insertion_tableau([[2, 2], []], [0, 2], 2, [[], [[1], [0]]], 2)
[[], [[1, 2], [0, 0]]]
sage: insertion_tableau([[2, 2], []], [2, 0], 2, [[], [[1, 0]]], 2)
[[], [[2, 0], [1, 0]]]
sage: insertion_tableau([[2, 2], [1]], [3, 0], 1, [[], []], 3)
[[1], [[1, 0], [0]]]
"""
psave = Partition(skp[1])
partc = skp[1] + [0]*(len(skp[0])-len(skp[1]))
tableau = SkewTableau(expr=tableau).to_expr()[1]
for k in range(len(tableau)):
tableau[-(k+1)] += [0]* ( skp[0][k] - partc[k] - len(tableau[-(k+1)]))
## We construct a tableau from the southwest corner to the northeast one
tableau = [[0] * (skp[0][k] - partc[k])
for k in reversed(range(len(tableau), len(skp[0])))] + tableau
tableau = SkewTableaux().from_expr([skp[1], tableau]).conjugate()
tableau = tableau.to_expr()[1]
skp = SkewPartition(skp).conjugate().to_list()
skp[1].extend( [0]*(len(skp[0])-len(skp[1])) )
if len(perm) > len(skp[0]):
return None
for k in range(len(perm)):
if perm[ -(k+1) ] !=0:
tableau[len(tableau)-len(perm)+k][ skp[0][len(perm)-(k+1)] - skp[1][ len(perm)-(k+1) ] - 1 ] = evaluation
return SkewTableau(expr=[psave.conjugate(),tableau]).conjugate().to_expr()
