The All-Thing

All stick and no carrot, since ought-three.

各位能夠讀中文得來賓您好。小的這還在學中文中,恐怕中文寫得不太好,希望你們還看得懂。


三衢道中 (曾幾)

梅子黃時日日晴,小溪泛盡卻山行。
綠陰不減來時路,添得黃鸝四五聲。

Contact:
| web page

Other views:
RSS 1.0
RSS 0.91
Plain (good for lynx)

Past posts:

October
Sun Mon Tue Wed Thu Fri Sat
     
9
 

Recent comments:
/computing/gateway.ecdt
/computing/linux.media.jukebox (2 days ago)

Recent search referers:
bit torrent fix (x2)
XIII fix crack
sims online prostitution crime
simply accounting bittorrent
Crack fix- xiii download
"The Overcoat" (x3)
pr0n torrent (x2)
XIII crack fix download (x2)
"XIII no cd"
Crack XIII
xiii crack
bit torrent chinese download
torrent xbox
dell x300 review
love's labour's lost bittorrent

Exits:
William's Aggregated Feeds



Creative Commons License
This work is licensed under a Creative Commons License.

       
Thu, 09 Oct 2003

Whitney Numbers

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 two-dimensional case, and pretty mind-bending for the three-dimensional case, but what about the generalization?

So we go to the Online Encyclopedia of Integer Sequences, type in (get this) 2, 4, 8 (the first three entries for the 3-d case) and lo and behold, we get:

http://www.research.att.com/projects/OEIS?Anum=A004070

Cool or what? (A complete fluke as their sequence is the table read by anti-diagonals... wtf?)

So anyways, the solution is

W(n,k)=if k=0 or n=0 then 1 else W(n,k-1)+W(n-1,k-1), 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

Gambler's Ruin Solution

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

Weird

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


   

My only love sprung from my only hate! Too early seen unknown, and known too late! -- William Shakespeare, "Romeo and Juliet"