Well, the frustration involving that small result I was trying to prove is over. It turns out that what we wanted to prove is only almost always true. Without getting into too many details, we were trying to prove something about a particular family of graphs, in fact, these graphs, and (to make a long story short) it's not always true. It's almost always true, but (and this will make more sense if you click those links above) it's not true when the number of triangles is 16. It's true for any other number (7? sure. 10,856,321? yep.) but not 16. Oy. Anyway, the way we found this out was actually by talking to another guy who was working on a similar (but more general) problem. He let us help him finish his paper, (which was very generous of him, because I know he could have done it himself) and the (much better than what we were originally trying to prove) result will likely soon be published. It's already up on arXiv, so feel free to check it out. So, we weren't able to prove exactly what we were trying to, but I'm still going to be published.
Sharayah tells me this is not really enough for a full blog post. I guess it's not interesting enough on its own. Or, at least, it's not very entertaining to read about. So. I will try to do better.
A few years ago (before this blog!) Sharayah and I went to New York the day before Thanksgiving. Why the day before, you ask? Isn't the parade the day after we went? Well, yes. We actually wandered around New York all night so we could get a really good spot to watch the parade. It was a really good time. You can read all about it here... oh right, it was before the blog. Well anyway, it was a good time and quite the adventure, so we're doing something similar this year. We're going up the day after Thanksgiving this year. Right. So, we're not watching the parade (at least not in person), but we're going to go explore all the fun Christmas stuff around the city like last time. And, unlike last time, there will probably be a blog post about it.
You can ask Sharayah about the title. It was her idea (I asked her for one, because I couldn't think of anything), but once she explained to me it made perfect sense.
you make beautiful things