def cardinality(self):
"""
The cardinality of ``self``
This is a Catalan number.
TESTS::
sage: BinaryTrees(0).cardinality()
1
sage: BinaryTrees(5).cardinality()
42
"""
return catalan_number(self._size)
def cardinality(self):
r"""
Returns the number of Dyck words of size n, i.e. the n-th Catalan
number.
EXAMPLES::
sage: DyckWords(4).cardinality()
14
sage: ns = range(9)
sage: dws = [DyckWords(n) for n in ns]
sage: all([ dw.cardinality() == len(dw.list()) for dw in dws])
True
"""
if self.k2 == self.k1:
return catalan_number(self.k1)
else:
return len(self.list())
def cardinality(self):
r"""
Returns the number of Dyck words of size n, i.e. the n-th Catalan
number.
EXAMPLES::
sage: DyckWords(4).cardinality()
14
sage: ns = range(9)
sage: dws = [DyckWords(n) for n in ns]
sage: all([ dw.cardinality() == len(dw.list()) for dw in dws])
True
"""
if self.k2 == self.k1:
return catalan_number(self.k1)
else:
return len(self.list())
def cardinality(self):
"""
The cardinality of ``self``
This is a Catalan number
TESTS::
sage: OrderedTrees(0).cardinality()
0
sage: OrderedTrees(1).cardinality()
1
sage: OrderedTrees(6).cardinality()
42
"""
if self._size == 0:
return Integer(0)
else:
return catalan_number(self._size-1)
def cardinality(self):
"""
The cardinality of ``self``
This is a Catalan number
TESTS::
sage: OrderedTrees(0).cardinality()
0
sage: OrderedTrees(1).cardinality()
1
sage: OrderedTrees(6).cardinality()
42
"""
if self._size == 0:
return Integer(0)
else:
return catalan_number(self._size - 1)
def cardinality(self):
"""
Returns the number of non-decreasing parking functions of size
`n`. This number is the `n`-th :func:`Catalan
number<sage.combinat.combinat.catalan_number>`.
EXAMPLES::
sage: PF = NonDecreasingParkingFunctions(0)
sage: PF.cardinality()
1
sage: PF = NonDecreasingParkingFunctions(1)
sage: PF.cardinality()
1
sage: PF = NonDecreasingParkingFunctions(3)
sage: PF.cardinality()
5
sage: PF = NonDecreasingParkingFunctions(5)
sage: PF.cardinality()
42
"""
return catalan_number(self.n)