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Partitions and Counting

Suppose that you have a set A with n elements. Is there a closed form solution of the number of ways that A can be partitioned in terms of n?

As an example, consider A = {a,b,c}. Then there are 5 different ways to partition this set.
1. a~a b~b c~c
2. a~b c~c
3. a~a b~c
4. a~c b~b
5. a~b~c

So I am trying to come up with some general formula for this. Even easier, there are 2 ways to partition a set with 2 elements, and only 1 way to partition a 1 element set.

Note by Oli Hohman
5 months, 2 weeks ago

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I think you are referring to the Bell numbers:

https://en.wikipedia.org/wiki/Bell_number

http://mathworld.wolfram.com/BellNumber.html

And if I understand correctly, there are only 2 ways to partition a set with two elements. Jon Haussmann · 5 months, 2 weeks ago

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@Jon Haussmann Thank you. I rushed in typing the last sentence, but I will edit that. Thank you! You found exactly what I was looking for. Oli Hohman · 5 months, 2 weeks ago

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