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Topic: the number of equivalence relations on {1,2, ...,n}
Replies: 8   Last Post: Nov 11, 2012 2:35 AM

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Robin Chapman

Posts: 281
Registered: 5/29/08
Re: the number of equivalence relations on {1,2, ...,n}
Posted: Nov 9, 2012 3:54 AM
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On 09/11/2012 06:09, quasi wrote:
> For n in N, let e(n) be the number of equivalence relations on
> the set {1,2,...,n}


Bell numbers:
http://en.wikipedia.org/wiki/Bell_number

> For n,k in N with k <= n, let f(n,k) be the number of equivalence
> relations on the set {1,2,...,n} with exactly k equivalence
> classes.


Stirling numbers:
http://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind





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