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Variable Set Distribution - Buckingham Pi Theorum

  1. Oct 6, 2014 #1
    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. jcsd
  3. Oct 7, 2014 #2

    Stephen Tashi

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    Science Advisor

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