mir.combinatorics: reviewers and ideas are wanted

[Timon Gehr via Digitalmars-d-announce]

On 28.03.2016 09:24, 9il wrote:
> Hello All,
>
> Sebastian Wilzbach (aka @greenify) starts mir.combinatorics.
>
> Numeric functions:
> - `binomial`
>
> Ranges:
> - `permutations` RoR
> - `cartesianPower` RoR
> - `combinations` RoR
> - `combinationsRepeat` RoR
>
> RoR - Range of Ranges
>
> PR: https://github.com/DlangScience/mir/pull/29
>
>
> Best regards,
> Ilya
>

Regarding ideas:
For each range, there should probably be a numeric function computing 
the length of that range. (e.g. here, binomial corresponds to 
combinations, there should be factorial corresponding to permutations etc.)

This table might provide some inspiration:
https://en.wikipedia.org/wiki/Twelvefold_way#Formulas

I'd suggest completing the set of functions and ranges such that they 
cover all cases in this table.
They can then be generalized. (E.g. instead of choosing a subset of a 
given size, one might want to choose multiple disjoint subsets of given 
sizes etc.)

Also (both numeric functions and ranges, often more than one range per 
numeric function):

- https://en.wikipedia.org/wiki/Multinomial_theorem
- https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind
- https://en.wikipedia.org/wiki/Derangement
- https://en.wikipedia.org/wiki/Cyclic_permutation, in particular 
transpositions
- https://en.wikipedia.org/wiki/Catalan_number

- https://en.wikipedia.org/wiki/Fuss%E2%80%93Catalan_number
- https://en.wikipedia.org/wiki/Narayana_number
- https://en.wikipedia.org/wiki/Delannoy_number
- https://en.wikipedia.org/wiki/Motzkin_number
- https://en.wikipedia.org/wiki/Schr%C3%B6der_number
- https://en.wikipedia.org/wiki/Schr%C3%B6der%E2%80%93Hipparchus_number
- ...