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Math Help - stirlings numbers 2nd kind? not sure

  1. #1
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    stirlings numbers 2nd kind? not sure

    Hi

    If i have a set (1,2,3,4)

    i want to split this into 2 sets. So the possible sets i can have are
    (1234)()
    (1)(234)
    (2)(134)
    (3)(124)
    (4)(123)
    (12)(34)
    (13)(24)
    (14)(23)

    so 8 sets

    my question is that what if i had a set with 32 elements or more

    Im thinking its just using stirlings numbers of the second kind for k=2. And then add 1 onto that (for the case with the empty sub set). But i wanted to confirm.

    many thanks for the help

    sam
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  2. #2
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    Quote Originally Posted by chogo View Post
    Hi

    If i have a set (1,2,3,4)

    i want to split this into 2 sets. So the possible sets i can have are
    (1234)()
    (1)(234)
    (2)(134)
    (3)(124)
    (4)(123)
    (12)(34)
    (13)(24)
    (14)(23)

    so 8 sets

    my question is that what if i had a set with 32 elements or more

    Im thinking its just using stirlings numbers of the second kind for k=2. And then add 1 onto that (for the case with the empty sub set). But i wanted to confirm.

    many thanks for the help

    sam
    If you have n elements then in general the number of such two sub-set partitions is 2^{n-1}.
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