# `CombSpace` and `Comb`¶

## `CombSpace`¶

class `CombSpace`(iterable_or_length, n_elements, *, slice_=None, perm_type=None)

A space of combinations.

This is a subclass of `PermSpace`; see its documentation for more details.

Each item in a `CombSpace` is a `Comb`, i.e. a combination. This is similar to `itertools.combinations()`, except it offers far, far more functionality. The combinations may be accessed by index number, the combinations can be of a custom type, the space may be sliced, etc.

Here is the simplest possible `CombSpace`:

```>>> comb_space = CombSpace(4, 2)
<CombSpace: 0..3, n_elements=2>
>>> comb_space
<Comb, n_elements=2: (0, 3)>
>>> tuple(comb_space)
(<Comb, n_elements=2: (0, 1)>, <Comb, n_elements=2: (0, 2)>,
<Comb, n_elements=2: (0, 3)>, <Comb, n_elements=2: (1, 2)>,
<Comb, n_elements=2: (1, 3)>, <Comb, n_elements=2: (2, 3)>)
```

The members are `Comb` objects, which are sequence-like objects that have extra functionality. (See documentation of `Comb` and its base class `Perm` for more info.)

## `Comb`¶

class `Comb`(perm_sequence, perm_space=None)

A combination of items from a `CombSpace`.

In combinatorics, a combination is like a permutation except with no order. In the `combi` package, we implement that by making the items in `Comb` be in canonical order. (This has the same effect as having no order because each combination of items can only appear once, in the canonical order, rather than many different times in many different orders like with `Perm`.)

Example:

```>>> comb_space = CombSpace('abcde', 3)
>>> comb = Comb('bcd', comb_space)
>>> comb
<Comb, n_elements=3: ('a', 'b', 'c')>
>>> comb_space.index(comb)
6
```

`PermSpace` and `Perm`