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

• Aug 31st 2010, 11:21 AM
emilbarton
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.
• Aug 31st 2010, 11:54 AM
Plato
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.
• Aug 31st 2010, 12:14 PM
undefined
Quote:

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
• Aug 31st 2010, 01:03 PM
emilbarton
By luck you found exactly what I was looking for! Thank you again!