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March 12th, 2009, 12:05 PM   #1
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Dividing n objects into groups

I am trying to find an equation or algorithm to find the number of ways to group n objects.
For example, f(5) can be divided 7 ways.
5 4 1 3 2 3 1 1 2 2 1 2 1 1 1 or 1 1 1 1 1

Also f(1)=1, f(2)=2, f(3)=3, f(4)=5.

I tried using 4 C 0 + 4 C 1 + ... 4 C 4 to count up the number of ways to choose spacings between groups but this leads to repeats such as 14, 23, 32, 41.

Any help would be appreciated and please ask if I'm not being clear in the wording.
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March 13th, 2009, 03:59 AM   #2
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What is the definition of "f(n)"? What do your strings of numbers indicate? How is "11111" a "division" of f(5)?

Thank you!
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March 13th, 2009, 05:31 AM   #3
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Re: Dividing n objects into groups

Check this out.
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March 13th, 2009, 06:54 AM   #4
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Re: Dividing n objects into groups

Thanks! That is it exactly. Too bad i dont have mathmatica though. I'll see if i can make any sense of it.
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