def from_expr(l):
"""
Returns a RibbonTableau from a MuPAD-Combinat expr for a skew
tableau. The first list in expr is the inner shape of the skew
tableau. The second list are the entries in the rows of the skew
tableau from bottom to top.
Provided primarily for compatibility with MuPAD-Combinat.
EXAMPLES::
sage: import sage.combinat.ribbon_tableau as ribbon_tableau
sage: sage.combinat.ribbon_tableau.from_expr([[1,1],[[5],[3,4],[1,2]]])
[[None, 1, 2], [None, 3, 4], [5]]
sage: type(_)
<class 'sage.combinat.ribbon_tableau.RibbonTableau_class'>
"""
return RibbonTableau_class(skew_tableau.from_expr(l)._list)
def from_expr(l):
"""
Returns a RibbonTableau from a MuPAD-Combinat expr for a skew
tableau. The first list in expr is the inner shape of the skew
tableau. The second list are the entries in the rows of the skew
tableau from bottom to top.
Provided primarily for compatibility with MuPAD-Combinat.
EXAMPLES::
sage: import sage.combinat.ribbon_tableau as ribbon_tableau
sage: sage.combinat.ribbon_tableau.from_expr([[1,1],[[5],[3,4],[1,2]]])
[[None, 1, 2], [None, 3, 4], [5]]
sage: type(_)
<class 'sage.combinat.ribbon_tableau.RibbonTableau_class'>
"""
return RibbonTableau_class(skew_tableau.from_expr(l)._list)
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()
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()