# Thread: stirlings numbers 2nd kind? not sure

1. ## 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

2. Originally Posted by chogo
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 $2^{n-1}$.