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The number of ways to express a specific summation

  1. Sep 1, 2010 #1
    Hello all,

    I have been thinking about a particular mathematical question (that I've made up) and I haven't been able to reach a solution yet..

    I want to find the rule for the function F(x,y) which gives the number of different "ways" that the integer x can be expressed as the summation of "y" pieces of integers (these integers have to be bigger than or equal to 1) (sorry for my awful technical English :))

    Let me clarify it with an example:

    When we consider F(9,4), it can be observed that

    9 = 1+1+1+6
    9 = 1+1+2+5
    9 = 1+1+3+4
    9 = 1+2+2+4
    9 = 1+2+3+3
    9 = 2+2+2+3

    Following from here, since there are 6 different ways of expressing this summation,
    F(9,4)=6

    In the above example, (1+1+1+6) and, for example, (1+6+1+1) are considered to be the same and thus are counted only once.


    NOTE: When we consider (1+1+1+6) and (1+6+1+1) to be different ways of summation, for instance, the problem becomes very easy and can be solved by pigeon hole principle. But the tricky part for me is to find a formula which considers the two expressions above and such to amount to the same.


    Thanks!
     
  2. jcsd
  3. Sep 1, 2010 #2
    The term you are looking for is "partition". So there's a starting point for you.
     
  4. Sep 2, 2010 #3
    Thank you very much adriank !
     
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