## 2012-06-29

“Bash it out.”

Also, last day to submit CUMC abstracts. So sleep deprived… don’t know if I can put anything coherent together…

EDIT: lol (I wrote this while bored in complex analysis). Its output:

# python incidence.py
IT HAS SIZE 64
IT HAS SIZE 64
IT HAS SIZE 32

I hate coding…

EDIT: So after a lot of computation, I determined that if we look at the dimensions of the cycle spaces of the complete graphs $K_n$, we actually get the sequence of triangular numbers (1, 3, 6, 10, 15, …). Although I don’t know why exactly… I can’t get a nice recursion; it seems difficult to deal with. I will probably write about this on my other blog once I’ve had some sleep.

EDIT: What a stupid way of computing the size of the cycle space, LOL. Just apply Gaussian elimination to the incidence matrix to find the dimension $n$ of its kernel. Then the size of $\mathcal{Z}(G)$ is $2^n$, of course.