def MultiSkewTableau(x):
"""
Returns a multi skew tableau object which is a tuple of skew
tableau.
EXAMPLES::
sage: s = MultiSkewTableau([ [[None,1],[2,3]], [[1,2],[2]] ])
sage: s.size()
6
sage: s.weight()
[2, 3, 1]
sage: s.shape()
[[[2, 2], [1]], [[2, 1], []]]
"""
if isinstance(x, MultiSkewTableau_class):
return x
return MultiSkewTableau_class([skew_tableau.SkewTableau(i) for i in x])
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.Partition(skp[1])
partc = skp[1] + [0] * (len(skp[0]) - len(skp[1]))
tableau = skew_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 = skew_tableau.from_expr([skp[1], tableau]).conjugate()
tableau = tableau.to_expr()[1]
skp = skew_partition.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 skew_tableau.SkewTableau(
expr=[psave.conjugate(), tableau]).conjugate().to_expr()