def __iter__(self):
"""
EXAMPLES::
sage: sp = SkewPartitions(3).list()
sage: SemistandardMultiSkewTableaux([SkewPartition([[1, 1, 1], []]), SkewPartition([[3], []])],[2,2,2]).list()
[[[[1], [2], [3]], [[1, 2, 3]]]]
::
sage: a = SkewPartition([[8,7,6,5,1,1],[2,1,1]])
sage: weight = [3,3,2]
sage: k = 3
sage: s = SemistandardMultiSkewTableaux(a.quotient(k),weight)
sage: len(s.list())
34
sage: RibbonTableaux(a,weight,k).cardinality()
34
"""
parts = self._shape
mu = self._weight
#Splitting the partition
s = [p.size() for p in parts]
parts = [p.to_list() for p in parts]
#Gluing the partitions
parttmp = parts[0]
i = 1
for i in range(1, len(parts)):
trans = parttmp[0][0]
current_part = parts[i]
current_part[1] += [0] * (len(current_part[0]) -
len(current_part[1]))
inner_current = [trans + j for j in current_part[1]]
outer_current = [trans + j for j in current_part[0]]
parttmp = [outer_current + parttmp[0], inner_current + parttmp[1]]
#List the corresponding skew tableaux
l = [st.to_word() for st in SemistandardSkewTableaux(parttmp, mu)]
S = SkewTableaux()
for k in range(len(l)):
pos = 0 #Double check this
restmp = [
S.from_shape_and_word(parts[0], [l[k][j] for j in range(s[0])])
]
for i in range(1, len(parts)):
w = [
l[k][j]
for j in range(pos + s[i - 1], pos + s[i - 1] + s[i])
]
restmp.append(S.from_shape_and_word(parts[i], w))
yield self.element_class(self, restmp)
def __init__(self, category=None):
"""
Initialize ``self``.
EXAMPLES::
sage: S = RibbonShapedTableaux()
sage: TestSuite(S).run()
"""
if category is None:
category = Sets()
SkewTableaux.__init__(self, category=category)
def __init__(self, category=None):
"""
Initialize ``self``.
EXAMPLES::
sage: S = RibbonShapedTableaux()
sage: TestSuite(S).run()
"""
if category is None:
category = Sets()
SkewTableaux.__init__(self, category=category)
def __iter__(self):
"""
EXAMPLES::
sage: sp = SkewPartitions(3).list()
sage: SemistandardMultiSkewTableaux([SkewPartition([[1, 1, 1], []]), SkewPartition([[3], []])],[2,2,2]).list()
[[[[1], [2], [3]], [[1, 2, 3]]]]
::
sage: a = SkewPartition([[8,7,6,5,1,1],[2,1,1]])
sage: weight = [3,3,2]
sage: k = 3
sage: s = SemistandardMultiSkewTableaux(a.quotient(k),weight)
sage: len(s.list())
34
sage: RibbonTableaux(a,weight,k).cardinality()
34
"""
parts = self._shape
mu = self._weight
#Splitting the partition
s = [ p.size() for p in parts ]
parts = [p.to_list() for p in parts]
#Gluing the partitions
parttmp = parts[0]
i = 1
for i in range(1,len(parts)):
trans = parttmp[0][0]
current_part = parts[i]
current_part[1] += [0]*(len(current_part[0])-len(current_part[1]))
inner_current = [ trans + j for j in current_part[1] ]
outer_current = [ trans + j for j in current_part[0] ]
parttmp = [ outer_current + parttmp[0], inner_current + parttmp[1] ]
#List the corresponding skew tableaux
l = [ st.to_word() for st in SemistandardSkewTableaux(parttmp, mu) ]
S = SkewTableaux()
for k in range(len(l)):
pos = 0 #Double check this
restmp = [ S.from_shape_and_word(parts[0], [l[k][j] for j in range(s[0])]) ]
for i in range(1, len(parts)):
w = [l[k][j] for j in range(pos+s[i-1], pos+s[i-1]+s[i])]
restmp.append( S.from_shape_and_word(parts[i], w) )
yield self.element_class(self, restmp)
def to_tableau(self):
r"""
Convert ``self`` to a :class:`SemistandardTableau`.
The :class:`SemistandardSkewTableau` is not implemented so this returns a :class:`SkewTableau`
EXAMPLES::
sage: pt = path_tableaux.SemistandardPathTableau([[],[3],[3,2],[3,3,1],[3,3,2,1],[4,3,3,1,0]])
sage: pt.to_tableau()
[[1, 1, 1, 5], [2, 2, 3], [3, 4, 5], [4]]
TESTS::
sage: SST = SemistandardTableaux(shape=[5,5,3],eval=[2,2,3,4,2])
sage: all(st == path_tableaux.SemistandardPathTableau(st).to_tableau() for st in SST)
True
"""
from sage.combinat.tableau import from_chain
if not self.is_integral():
raise ValueError(
f"{self} must have all entries nonnegative integers")
lt = [[i for i in a if i > 0] for a in self]
if self.is_skew():
return SkewTableaux().from_chain(lt)
else:
return from_chain(lt)
def from_expr(self, l):
"""
Return a :class:`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: RibbonTableaux().from_expr([[1,1],[[5],[3,4],[1,2]]])
[[None, 1, 2], [None, 3, 4], [5]]
"""
return self.element_class(self, SkewTableaux().from_expr(l))
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 __init__(self, st):
r"""
sage: from sage.combinat.skew_tableau import SkewTableau
sage: from jeudetaquin import JeuDeTaquin
sage: jdt = JeuDeTaquin([[None,2,3],[None,4],[5]]) ; jdt
5
. 4
. 2 3
sage: jdt.done(), jdt.has_hole()
(False, False)
sage: jdt.create_hole((0,0))
Traceback (most recent call last):
...
ValueError: corner must be an inner corner
sage: jdt.create_hole((1,0))
sage: jdt
5
* 4
. 2 3
sage: jdt.done(), jdt.has_hole()
(False, True)
sage: jdt.slide(); jdt
5
4
. 2 3
sage: jdt.done(), jdt.has_hole()
(False, False)
sage: jdt.slide()
Traceback (most recent call last):
...
ValueError: There is no hole
sage: jdt.create_hole((0,0)); jdt
5
4
* 2 3
sage: jdt.done(), jdt.has_hole()
(False, True)
sage: jdt.slide(); jdt
5
4
2 * 3
sage: jdt.done(), jdt.has_hole()
(False, True)
sage: jdt.create_hole((0,1))
Traceback (most recent call last):
...
ValueError: There is already a hole at (0, 1)
sage: jdt.slide(); jdt
5
4
2 3
sage: jdt.done(), jdt.has_hole()
(True, False)
sage: t = SkewTableau([[None,None,None,None,2,3,7,8],[None,None,4,9],[None,5,6],[10]])
sage: jdt = JeuDeTaquin(t); jdt
10
. 5 6
. . 4 9
. . . . 2 3 7 8
sage: jdt.create_hole((0, 3)); jdt
10
. 5 6
. . 4 9
. . . * 2 3 7 8
sage: jdt.slide(); jdt
10
. 5 6
. . 4 9
. . . 2 * 3 7 8
sage: jdt.slide(); jdt
10
. 5 6
. . 4 9
. . . 2 3 * 7 8
sage: jdt.slide(); jdt
10
. 5 6
. . 4 9
. . . 2 3 7 * 8
sage: jdt.slide(); jdt
10
. 5 6
. . 4 9
. . . 2 3 7 8
sage: jdt.create_hole((1, 1)); jdt
10
. 5 6
. * 4 9
. . . 2 3 7 8
sage: jdt.slide(); jdt
10
. 5 6
. 4 * 9
. . . 2 3 7 8
sage: jdt.slide(); jdt
10
. 5
. 4 6 9
. . . 2 3 7 8
sage: jdt.create_hole((2, 0)); jdt
10
* 5
. 4 6 9
. . . 2 3 7 8
sage: jdt.slide(); jdt
10
5
. 4 6 9
. . . 2 3 7 8
sage: jdt.create_hole((0, 2)); jdt
10
5
. 4 6 9
. . * 2 3 7 8
sage: jdt.slide(); jdt
10
5
. 4 6 9
. . 2 * 3 7 8
sage: jdt.slide(); jdt
10
5
. 4 6 9
. . 2 3 * 7 8
sage: jdt.slide(); jdt
10
5
. 4 6 9
. . 2 3 7 * 8
sage: jdt.slide(); jdt
10
5
. 4 6 9
. . 2 3 7 8
sage: jdt.create_hole((0, 1)); jdt
10
5
. 4 6 9
. * 2 3 7 8
sage: jdt.slide(); jdt
10
5
. 4 6 9
. 2 * 3 7 8
sage: jdt.slide(); jdt
10
5
. 4 6 9
. 2 3 * 7 8
sage: jdt.slide(); jdt
10
5
. 4 6 9
. 2 3 7 * 8
sage: jdt.slide(); jdt
10
5
. 4 6 9
. 2 3 7 8
sage: jdt.create_hole((1, 0)); jdt
10
5
* 4 6 9
. 2 3 7 8
sage: jdt.slide(); jdt
10
5
4 * 6 9
. 2 3 7 8
sage: jdt.slide(); jdt
10
5
4 6 * 9
. 2 3 7 8
sage: jdt.slide(); jdt
10
5
4 6 9
. 2 3 7 8
sage: jdt.create_hole((0, 0)); jdt
10
5
4 6 9
* 2 3 7 8
sage: jdt.slide(); jdt
10
5
4 6 9
2 * 3 7 8
sage: jdt.slide(); jdt
10
5
4 6 9
2 3 * 7 8
sage: jdt.slide(); jdt
10
5
4 6 9
2 3 7 * 8
sage: jdt.slide(); jdt
10
5
4 6 9
2 3 7 8
"""
super(JeuDeTaquin, self).__init__(SkewTableaux(), st)
self._hole = None
self._new_st = None