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Thu, 09 Oct 2003 This was cool. I've been working on a problem at work and at one point we needed to find the maximum number of ways of dividing an /n/dimensional space into k partitions. It's easy enough to figure this out for the one and twodimensional case, and pretty mindbending for the threedimensional case, but what about the generalization? So we go to the Online Encyclopedia of Integer Sequences, type in (get this) http://www.research.att.com/projects/OEIS?Anum=A004070 Cool or what? (A complete fluke as their sequence is the table read by antidiagonals... wtf?) So anyways, the solution is W(n,k)=if k=0 or n=0 then 1 else W(n,k1)+W(n1,k1), or W(n,k)=Sum(binomial(k,i), i=0..n) if you were curious (so order exponential, unfortunately for us). Posted at 13:38  /math  (leave a comment)  permalink 

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