# Math::Combinatorics

This module provides a few functions for generating combinatoric sequences.

## USAGE

The functions in this module can be selectively imported, eg.

```
use Math::Combinatorics < multicombinations variations >;
```

Or you can import everything with the `:ALL`

tag

```
use Math::Combinatorics :ALL;
```

## FUNCTIONS

### multicombinations

Also known as 'combinations with replacement', 'k-multicombinations', or 'multisubsets'

say multicombinations(<A B C D>, 2); # OUTPUT: ((A A) (A B) (A C) (A D) (B B) (B C) (B D) (C C) (C D) (D D))

Implemented in NQP

### variations

Also known as 'k-permutations of n'. I opted to give this the more archaic name of `variations`

rather than creating a multi of `permutations`

.

say variations(<A B C D>, 2); # OUTPUT: ((A B) (A C) (A D) (B A) (B C) (B D) (C A) (C B) (C D) (D A) (D B) (D C))

Implemented in NQP

### partitions

Also known as 'integer partitions'.

say partitions(5); # OUTPUT: ((1 1 1 1 1) (1 1 1 2) (1 1 3) (1 2 2) (1 4) (2 3) (5))

Implemented in NQP

### derangements

Essentially the permutations where no element is in it's original place

say derangements(<A B C D>) # OUTPUT: ((B A D C) (B C D A) (B D A C) (C A D B) (C D A B) (C D B A) (D A B C) (D C A B) (D C B A))

implemented in Raku

### factorial and subfactorial

Since several functions rely on getting the factorial (or subfactorial) of a number, I have those functions defined as well.

say factorial(6); # OUTPUT: 720 say subfactorial(6); # OUTPUT: 256

## NOTES

The goal of this module is to be something similar to Perl's Algorithm::Combinatorics, implemented in NQP for fast performance. Not all functions are implemented in NQP, and if there's a function you'd like to add, I'm happy to accept pull requests for more algorithms, even in pure Raku. I - or others - can always work towards translating them to NQP later as time permits.

## CAVEATS & LIMITATIONS

I held off on publishing this module for many years because I wanted to polish it, provide more functions, and implement faster `.skip`

on things like `permutations`

(where the n-th permutation in a sequence can be determined algorithmically). Unfortunately, I have learned that my life doesn't always permit the long periods of time to dedicate to this.

My skill with NQP is that of a amateur, so I may not have written the *most* efficient code, however the implementations written in NQP should at least be noticeably faster than most pure-Raku functions implementing the same algorithms.

As always - pull requests are welcome, both for new functions, and improvements to the existing ones.

## LICENSE

```
The Artistic License 2.0
```

See LICENSE file in the repository for the full license text.