Pythonic package for combinatorics
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Combi is a Pythonic package for combinatorics.

Combi lets you explore spaces of permutations and combinations as if they were Python sequences, but without generating all the permutations/combinations in advance. It lets you specify a lot of special conditions on these spaces. It also provides a few more classes that might be useful in combinatorics programming.

Combi is released under the MIT license.

Combi documentation:

Combi on GitHub:

Combi on PyPI:


Basic usage

Use PermSpace to create a permutation space:

>>> from combi import *
>>> perm_space = PermSpace('meow')

It behaves like a sequence:

>>> len(perm_space)
>>> perm_space[7]
<Perm: ('e', 'm', 'w', 'o')>
>>> perm_space.index('mowe')

And yet the permutations are created on-demand rather than in advance.

Use CombSpace to create a combination space, where order doesn't matter:

>>> comb_space = CombSpace(('vanilla', 'chocolate', 'strawberry'), 2)
>>> comb_space
<CombSpace: ('vanilla', 'chocolate', 'strawberry'), n_elements=2>
>>> comb_space[2]
<Comb, n_elements=2: ('chocolate', 'strawberry')>
>>> len(comb_space)

For more details, try the tutorial or see the documentation contents.


  • PermSpace lets you explore a space of permutations as if it was a Python sequence.
    • Permutations are generated on-demand, so huge permutation spaces can be created easily without big memory footprint.
    • PermSpace will notice if you have repeating elements in your sequence, and treat all occurences of the same value as interchangable rather than create redundant permutations.
    • A custom domain can be specified instead of just using index numbers.
    • You may specify some elements to be fixed, so they'll point to the same value in all permutations. (Useful for limiting an experiment to a subset of the original permutation space.)
    • Permutation spaces may be limited to a certain degree of permutations. (A permutation's degree is the number of transformations it takes to make it.)
    • k-permutations are supported.
    • You may specify a custom type for the generated permutations, so you could implement your own functionality on them.
  • CombSpace lets you explore a space of combinations as if it was a Python sequence.
  • MapSpace is like Python's built-in map, except it's a sequence that allows index access.
  • ProductSpace is like Python's itertools.product, except it's a sequence that allows index access.
  • ChainSpace is like Python's itertools.chain, except it's a sequence that allows index access.
  • SelectionSpace is a space of all selections from a sequence, of all possible lengths.
  • The Bag class is a multiset like Python's collections.Counter, except it offers far more functionality, like more arithmetic operations between bags, comparison between bags, and more. (It can do that because unlike Python's collections.Counter, it only allows natural numbers as keys.)
  • Classes FrozenBag, OrderedBag and FrozenOrderedBag are provided, which are variations on Bag.



Use pip to install Combi:

$ pip install combi


Combi on GitHub: Feel free to fork and send pull requests!

There are three Combi groups, a.k.a. mailing lists:

Combi was created by Ram Rachum. I provide Development services in Python and Django.