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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.

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# Variable Set Distribution - Buckingham Pi Theorum

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