# Thread: How to get the cardinality of a set of partitions?

1. ## How to get the cardinality of a set of partitions?

Hello,

I would like to know how to obtain the cardinality of a set of partitions for the given cardinality of another set. For example, given a set of 4 elements, I obtain the following set of 5 partitions with their subset cardinalities ranging over indices from 1 to 4:
0 0 0 1
0 2 0 0
1 0 1 0
2 1 0 0
4 0 0 0
I'd like to know the name of this set too. Thank you in advance for your help.

2. I must tell you that I have no idea what you post is saying.
However Stirling numbers of the second kind and Bell Numbers may be of some use to you.

3. Originally Posted by emilbarton
Hello,

I would like to know how to obtain the cardinality of a set of partitions for the given cardinality of another set. For example, given a set of 4 elements, I obtain the following set of 5 partitions with their subset cardinalities ranging over indices from 1 to 4:

0 0 0 1
0 2 0 0
1 0 1 0
2 1 0 0
4 0 0 0

I'd like to know the name of this set too. Thank you in advance for your help.
I also can't make sense of this, but it seems you are after this function:

Partition Function P -- from Wolfram MathWorld

4. By luck you found exactly what I was looking for! Thank you again!