Combinatics

Set Partitions

calcpy.bellpartition(values)

Get possible paritions of values.

Parameters:

values (list | tuple | set) – Values to partition.

Yields:

list[list | tuple | set] – Parition of values

See also

https://docs.sympy.org/latest/modules/functions/combinatorial.html#sympy.functions.combinatorial.numbers.bell https://oeis.org/A000110

Examples

Partition a list.

>>> for partition in bellpartition([0, 1, 2]):
...     print(partition)
[[0, 1, 2]]
[[0], [1, 2]]
[[0, 1], [2]]
[[0, 2], [1]]
[[0], [1], [2]]

Partition a tuple.

>>> for partition in bellpartition(("a", "b", "c", "d")):
...     print(partition)
[('a', 'b', 'c', 'd')]
[('a',), ('b', 'c', 'd')]
[('a', 'b'), ('c', 'd')]
[('a', 'c', 'd'), ('b',)]
[('a',), ('b',), ('c', 'd')]
[('a', 'b', 'c'), ('d',)]
[('a', 'd'), ('b', 'c')]
[('a',), ('b', 'c'), ('d',)]
[('a', 'b', 'd'), ('c',)]
[('a', 'c'), ('b', 'd')]
[('a',), ('b', 'd'), ('c',)]
[('a', 'b'), ('c',), ('d',)]
[('a', 'c'), ('b',), ('d',)]
[('a', 'd'), ('b',), ('c',)]
[('a',), ('b',), ('c',), ('d',)]

Partition a set.

>>> for partition in bellpartition({False, True}):
...     print(partition)
[{False, True}]
[{False}, {True}]