I submitted my application for the National Science Foundation graduate fellowship at around 7:00 this morning. This nearly ends an extremely hectic week, likely to be the most hectic of the quarter. The only thing remaining is the dreadful GRE subject test tomorrow. I am rewarding myself by going to hear Musica Antiqua Köln perform Heinichen, Zelenka, and Telemann on Sunday. It will be interesting to see which way Reinhard Goebel plays the violin nowadays.
I have been enjoying my combinatorics class a lot lately. If nothing else, it has been providing evidence that I have actually learned something in college. (That’s a good thing for a senior, right?) But posets are also fun on their own. We were talking about incidence algebras yesterday, and they’re really interesting. My intuition says that incidence algebras essentially tell you everything about a poset that a Dirichlet series can tell you about the integers, especially if we represent the integers by an appropriate Hasse diagram. (That’s probably just about everything, for the record.) For example, if you want to know the number of length k chains between two elements of a poset, I can easily write down an element of the incidence algebra that will tell you that immediately.