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Sum of subsets

  1. Jun 13, 2010 #1
    Dear Friends,

    I have a question and would be pleased if you help me by suggesting a paper or book to study.

    Let A={1,2,....,n}. We consider all the subsets with k elements. How many of these sets have a sum of r ?
    e.g.
    for n=6, k=3, r=10

    {1,3,6}

    {1,4,5}

    {2,3,5}
    Hense the solution in this case is 3.

    Thanks for your kind.
     
  2. jcsd
  3. Jun 15, 2010 #2
    Maybe this helps: http://en.wikipedia.org/wiki/Partition_(number_theory)" [Broken]
     
    Last edited by a moderator: May 4, 2017
  4. Jul 19, 2010 #3
    It's the binomial coefficient (r-1) C (k-1).
     
  5. Aug 18, 2010 #4
    Generating Function of your number

    soroush1358, I have answer your question in this post: http://www.voofie.com/content/144/sum-of-subsets-with-k-elements-having-a-total-sum-of-r/" [Broken].

    You can read more Mathematics related articles in http://www.voofie.com/concept/Mathematics/" [Broken].

    In short, the generating function of your number is:

    [tex]G_n(x,y) &= (1+x y)(1+x^2 y)(1+x^3 y)...(1+x^n y) \\ &= \prod_{r=1}^n (1+x^r y) \end{align*}[/tex]
     
    Last edited by a moderator: May 4, 2017
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