Ejemplo n.º 1
0
    def cardinality(self):
        """
        EXAMPLES::

            sage: from sage.combinat.restricted_growth import RestrictedGrowthArrays
            sage: R = RestrictedGrowthArrays(6)
            sage: R.cardinality()
            203
        """
        return bell_number(self._n)
Ejemplo n.º 2
0
    def cardinality(self):
        """
        EXAMPLES::

            sage: from sage.combinat.restricted_growth import RestrictedGrowthArrays
            sage: R = RestrictedGrowthArrays(6)
            sage: R.cardinality()
            203
        """
        return bell_number(self._n)
Ejemplo n.º 3
0
    def _gs_iterator(self, base_ring):
        r"""
        EXAMPLES::

            sage: P = species.PartitionSpecies()
            sage: g = P.generating_series()
            sage: g.coefficients(5)
            [1, 1, 1, 5/6, 5/8]
        """
        from sage.combinat.combinat import bell_number
        for n in _integers_from(0):
            yield self._weight*base_ring(bell_number(n)/factorial_stream[n])
Ejemplo n.º 4
0
    def _gs_iterator(self, base_ring):
        r"""
        EXAMPLES::

            sage: P = species.PartitionSpecies()
            sage: g = P.generating_series()
            sage: g.coefficients(5)
            [1, 1, 1, 5/6, 5/8]
        """
        from sage.combinat.combinat import bell_number
        for n in _integers_from(0):
            yield self._weight*base_ring(bell_number(n)/factorial_stream[n])
Ejemplo n.º 5
0
    def cardinality(self):
        """
        Return the number of set partitions of the set `S`.

        The cardinality is given by the `n`-th Bell number where `n` is the
        number of elements in the set `S`.

        EXAMPLES::

            sage: SetPartitions([1,2,3,4]).cardinality()
            15
            sage: SetPartitions(3).cardinality()
            5
            sage: SetPartitions(3,2).cardinality()
            3
            sage: SetPartitions([]).cardinality()
            1
        """
        return bell_number(len(self._set))
Ejemplo n.º 6
0
    def cardinality(self):
        """
        Return the number of set partitions of the set `S`.

        The cardinality is given by the `n`-th Bell number where `n` is the
        number of elements in the set `S`.

        EXAMPLES::

            sage: SetPartitions([1,2,3,4]).cardinality()
            15
            sage: SetPartitions(3).cardinality()
            5
            sage: SetPartitions(3,2).cardinality()
            3
            sage: SetPartitions([]).cardinality()
            1
        """
        return bell_number(len(self._set))