Way to compute Stirling numbers of the second kind from a multiset

Asked Dec 30 '14 at 06:48

Active Jan 01 '15 at 09:31

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I was wondering what algorithm would compute

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

Where

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.

asked Dec 30 '14 at 06:48

robertkin

What is the problem that you are trying to solve? – Kirill Dec 30 '14 at 07:24
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. – robertkin Dec 30 '14 at 21:18
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? – Kirill Dec 30 '14 at 22:02
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 – robertkin Dec 31 '14 at 01:38
Interesting question, but probably better suited for the math stackexchange. – Nick Alger Dec 31 '14 at 07:48
Yes, this is a combinatorics question, not a computational one. – Wolfgang Bangerth Dec 31 '14 at 13:45
This question appears to be off-topic because it is about combinatorics. – Wolfgang Bangerth Dec 31 '14 at 13:45
Possible duplicate? http://math.stackexchange.com/q/16890/23353 (I didn't spend enough time to compare.) – apnorton Jan 29 '15 at 05:29

Way to compute Stirling numbers of the second kind from a multiset

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