I was wondering what algorithm would compute

S(n, k {occurences of each element})  


S(6, 3, {1, 2, 3} )

would give the total number of ways a set with 6 elements in which 3 are the same element and a different 2 are another element (and 1 is its unique element) could be split into 3 non-empty sets, ignoring permutations.

This is basically the extension of Stirling numbers of the second kind to deal with multisets.

  • $\begingroup$ What is the problem that you are trying to solve? $\endgroup$ – Kirill Dec 30 '14 at 7:24
  • $\begingroup$ How to compute number of unique ways to split a multiset into a given number of non-empty subsets. Ignore permutations, and treat all repeated elements as identical. $\endgroup$ – robertkin Dec 30 '14 at 21:18
  • $\begingroup$ No, that's not my question. What is the actual problem that gave rise to this question? Why is this particular combinatorics question of interest? $\endgroup$ – Kirill Dec 30 '14 at 22:02
  • $\begingroup$ I was simply learning about stirling numbers and was thinking about how to expand it to deal with repeated elements. There's no general formula for it, so I was looking for an algorithm to do so $\endgroup$ – robertkin Dec 31 '14 at 1:38
  • $\begingroup$ Interesting question, but probably better suited for the math stackexchange. $\endgroup$ – Nick Alger Dec 31 '14 at 7:48

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