• 9il (13/13) Mar 28 2016 Hello All,
• jmh530 (2/3) Mar 28 2016 Cool, when I have time I will take a look.
• Timon Gehr (27/40) Mar 28 2016 Regarding ideas:
• jmh530 (15/20) Mar 28 2016 I agree. I had been looking at the Discrete Math toolbox for
• Seb (2/8) Mar 29 2016 Thanks a lot for your input and ideas - I will work on it ;-)

9il <ilyayaroshenko gmail.com> writes:

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

jmh530 <john.michael.hall gmail.com> writes:

On Monday, 28 March 2016 at 07:24:12 UTC, 9il wrote:
 Sebastian Wilzbach (aka  greenify) starts mir.combinatorics.

Cool, when I have time I will take a look.

Timon Gehr <timon.gehr gmx.ch> writes:

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
- ...

jmh530 <john.michael.hall gmail.com> writes:

On Monday, 28 March 2016 at 15:30:56 UTC, Timon Gehr wrote:
 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.)

I agree. I had been looking at the Discrete Math toolbox for 
Matlab to compare functionality and factorial seemed worth adding 
(as an aside, I saw an earlier thread about adding factorial to 
std.math and people were like nobody uses factorial and I wanted 
to punch my computer screen). Matlab's toolbox also has gcd, lcm, 
and some prime number functions.

I'm not entirely sold on the name of the binomial function. I'm 
concerned if it will be confusing if working with other 
dlangscience projects. Looking at dstats there are a bunch of 
functions with binomial in the name (rBinomial, binomialCDF, 
etc.). SciPy/SAS uses comb. Matlab uses nchoosek. R uses combn. 
I'm not a fan of combn.

Other potential overlapping functionality: logFactorial, 
logNcomb, Perm, perm, Comb, comb.

Seb <seb wilzba.ch> writes:

On Monday, 28 March 2016 at 15:30:56 UTC, Timon Gehr wrote:
 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:

Thanks a lot for your input and ideas - I will work on it ;-)