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Re: Can this be explained in layman's terms?by jaredor (Priest) 
on Jan 14, 2017 at 07:27 UTC ( #1179559=note: print w/replies, xml )  Need Help?? 
Hi BrowserUk, I'm a lackluster mathematics student, but perhaps I can volunteer an explanation that doesn't stray too far from the rigor. First, I think I would like to recast your statement as "For any set of n elements the number of ways to partition the set into k nonempty subsets is denoted S(n,k) and these numbers are known as Stirling numbers of the second kind."
Sometimes the rule S(n,k) = 0 if k>n is given for completeness, i.e., you can't partition something up into more nonempty subsets than for which it has elements, but this is considered obvious and you won't run into the need for it if you start with any reasonable case where n>=k.
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