Dear all,
suppose that I have N distinct elements, I would like to count the number of ways that they can be arranged in subsets of cardinality m1,m2,...,mK such that m1+m2+...+mK = N.
Example: I have N=4 elements, and I want to count the number of partitions of cardinality [2,1,1], that is
{1,2}{3}{4}
{1,3}{2}{4}
{1,4}{2}{3}
{2,3}{1}{4}
{2,4}{1}{3}
{3,4}{1}{2}
=6
Is there any general formula to compute this number?
Many thanks.
Number of unordered partitions of a given cardinality

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Re: Number of unordered partitions of a given cardinality
Stirling numbers of the first and second kind would help I suppose...
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Re: Number of unordered partitions of a given cardinality
If I understand correctly, what you are looking for is probably https://en.wikipedia.org/wiki/Multinomial_theorem.