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Math Help - Partitions proof

  1. #1
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    Partitions proof

    Let the number of partitions of n into parts each less than or equal to m be denoted P(n,m). Prove
    P(n,m) = P(n, m-1) + P(n-m,m)
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    Re: Partitions proof

    Quote Originally Posted by BlinkyBoo View Post
    Let the number of partitions of n into parts each less than or equal to m be denoted P(n,m). Prove
    P(n,m) = P(n, m-1) + P(n-m,m)
    I have written on this question. So I tell you whoever wrote your question has left out some cases.
    What happens if m=1~? What happens if m=n~?

    Here is the MathCad way of doing it.
    [ATTACH=CONFIG]23869[/ATTACH]
    Attached Thumbnails Attached Thumbnails Partitions proof-untitled.gif  
    Last edited by Plato; May 14th 2012 at 03:44 PM.
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    Re: Partitions proof

    what is mathcad? >.> ... i'm not really following that equation
    I'm a little confused because there is a formula in the book about partitioning n into exactly r parts where order counts = C(n-1,r-1)
    but then there's another one that says "the number of ways of writing n as the sum of r or fewer integers where the order of the summands matters is C(r+n-1,n)"
    but i didn't think they applied because order shouldn't count, should it?
    I was also trying to play with the concept that the number of partitions of n into r or less parts = the number of partitions of n into parts that are r or less, but have gotten nowhere so far :\

    Quote Originally Posted by Plato View Post
    What happens if
    if m = 1 there should only be one partition, n itself, right?
    and if m = n, then all the partitions = 1
    Last edited by BlinkyBoo; May 14th 2012 at 06:50 PM.
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    Re: Partitions proof

    could you be more specific please?
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    Re: Partitions proof

    Quote Originally Posted by BlinkyBoo View Post
    could you be more specific please?
    You can study this web page.
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