def cardinality(self):
"""
EXAMPLES::
sage: SemistandardSkewTableaux([[2,1],[]]).cardinality()
8
"""
count = 0
for mu in IntegerVectors(self.p.size(), self.p.size()):
count += SemistandardSkewTableaux_pmu(self.p, mu).cardinality()
return count
def __iter__(self):
"""
EXAMPLES::
sage: Combinations(['a','a','b'],2).list() # indirect doctest
[['a', 'a'], ['a', 'b']]
"""
items = map(self.mset.index, self.mset)
indices = uniq(sorted(items))
counts = [0] * len(indices)
for i in items:
counts[indices.index(i)] += 1
for iv in IntegerVectors(self.k, len(indices), outer=counts):
yield sum([[self.mset[indices[i]]] * iv[i]
for i in range(len(indices))], [])
def __iter__(self):
"""
TESTS::
sage: LyndonWords(3,3).list() # indirect doctest
[word: 112, word: 113, word: 122, word: 123, word: 132, word: 133, word: 223, word: 233]
"""
for c in IntegerVectors(self.k, self.n):
cf = [x for x in c if x != 0]
nonzero_indices = []
for i in range(len(c)):
if c[i] != 0:
nonzero_indices.append(i)
for lw in LyndonWords_evaluation(cf):
yield LyndonWord(map(lambda x: nonzero_indices[x-1]+1, lw), check=False)
def __iter__(self):
"""
EXAMPLES::
sage: SemistandardSkewTableaux([[2,1],[]]).list() #indirect test
[[[1, 1], [2]],
[[1, 1], [3]],
[[1, 2], [2]],
[[1, 3], [2]],
[[1, 2], [3]],
[[1, 3], [3]],
[[2, 2], [3]],
[[2, 3], [3]]]
"""
for mu in IntegerVectors(self.p.size(), self.p.size()):
for ssst in SemistandardSkewTableaux_shape_weight(self.p, mu):
yield ssst
def __iter__(self):
"""
TESTS::
sage: LyndonWords(3,3).list() # indirect doctest
[word: 112, word: 113, word: 122, word: 123, word: 132, word: 133, word: 223, word: 233]
"""
for c in IntegerVectors(self._k, self._n):
cf = []
nonzero_indices = []
for i, x in enumerate(c):
if x:
nonzero_indices.append(i)
cf.append(x)
for lw in LyndonWords_evaluation(Composition(cf)):
yield self._words([nonzero_indices[x - 1] + 1 for x in lw],
check=False)
