# Variable Set Distribution - Buckingham Pi Theorum

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1. Oct 6, 2014

### SSGD

Background:

I am trying to write a program for Buckingham Pi Groups. I need to find a way to list all the input varialbes as different sets.

For example if I have 4 variables [V D p u] and I want to distribute them 3 ways I get 4 sets.

Number of Sets = Binomial(Number of Variables, Variables per Set) = Binomial(4, 3) = 4
Set1 = [V D p]
Set2 = [V D u]
Set3 = [V p u]
Set4 = [D p u]

For example if I have 4 variables [V D p u] and I want to distribute them 2 ways I get 6 sets.

Number of Sets = Binomial(Number of Variables, Variables per Set) = Binomial(4, 2) = 6
Set1 = [V D]
Set2 = [V p]
Set3 = [V u]
Set4 = [D p]
Set5 = [D u]
Set6= [p u]

Can the different Sets be created by a matrix product?

[V D p u]x(4xN)=(1xN)

First Example
(1x4)x(4x3)=(1x3)
or
(4x4)x(4x3)=(4x3)

Second Example
(1x4)x(4x2)=(1x2)
or
(6x4)x(4x2)=(6x2)

Is anyone familiar with this kind of manipulation of Sets of Variables. I need help with the math or programming that can solve for the different sets. I have experience with matrix math and programming, but I just can't figure this problem out.

2. Oct 7, 2014