Lunchtime blog

For some reason John and I (quite independently) got lunch early so I'm now left with half an hour to kill. What better way to do it than by spouting random nonsense?

So, what to talk about? Maybe now would be a good time to talk about the PhD, as I haven't really updated anyone on it for a while.

Unfortunately, it is going rather slowly for my liking. The fact I haven't been on top form for some time hasn't helped, then again nor has the fact that it's actually quite hard. As one would expect.

Presently, I am looking at objects called uniquely solvable puzzles . These are a set of rows of numbers which satisfy a certain property (when you rearrange the set, one of the elements in a row has to change, essentially). The theory is that if you can find that if the row has length k, we can find a large number of rows that satisfy the property. This will eventually lower the matrix exponent (see previous entry "what I actually do" for details), although perhaps not to 2 as is hoped.

Another thing I am looking at is linked to this, and concerns how you can split the set of numbers 1...3k into three sets of size k, satisfying a certain property. Showing that this property holds for a large number k will also yield an exponent of 2 (and probably get me the Fields Medal, since it's not an easy problem to solve).

So that's where I am just now. Before I get back to work though, I have some tutorial work to mark. Aaah the joy...