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
- ...

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