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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 My language exchange partner and I were going over the Gambler's Ruin problem yesterday (he is a big random walk guy and yes, this is the type of stuff we end up talking about in the English portion) and we came up with a solution remarkably similar to this one I found today: http://www.quantnotes.com/edutainment/betting/gamblersruin.htm No random walks involved, just straight recurrence solving. Interesting that there's a hidden q != p assumption in there (which we didn't notice and had us scratching our heads as to why everything collapsed to 0/0 in the q = p case.) Posted at 13:30  /math  (leave a comment)  permalink I swear to god I just heard a Grappelli sample in the middle of some random hiphop track. Posted at 13:23  /media/music  (leave a comment)  permalink 

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