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 __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)
