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Math Help - How to get the cardinality of a set of partitions?

  1. #1
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    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.
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  2. #2
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    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.
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  3. #3
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    Quote Originally Posted by emilbarton View Post
    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
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  4. #4
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    By luck you found exactly what I was looking for! Thank you again!
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